To simplify the expression, we will distribute and combine like terms.
First, we distribute 6 to (3x - 5):
6(3x - 5) = 18x - 30
Next, we distribute 2 to (3x - 5):
2(3x - 5) = 6x - 10
Finally, we distribute -8 to (2x - 5):
-8(2x - 5) = -16x + 40
Putting it all together, the expression becomes:
18x - 30 + 6x - 10 - 16x + 40
Simplifying further:
(18x + 6x - 16x) + (-30 - 10 + 40)
8x + 0
The simplified expression is 8x.
Simplify the expression.
6(3x−5)+2(3x−5)−8(2x−5)
42 answers
Write an equation and solve for the unknown number.
Twice a number, increased by 3 is 7.
Twice a number, increased by 3 is 7.
Let the unknown number be represented by "x".
The equation can be written as:
2x + 3 = 7
To solve for x, we will isolate it on one side of the equation.
First, we subtract 3 from both sides of the equation:
2x + 3 - 3 = 7 - 3
This simplifies to:
2x = 4
Next, we divide both sides of the equation by 2:
(2x)/2 = 4/2
This simplifies to:
x = 2
Therefore, the unknown number is 2.
The equation can be written as:
2x + 3 = 7
To solve for x, we will isolate it on one side of the equation.
First, we subtract 3 from both sides of the equation:
2x + 3 - 3 = 7 - 3
This simplifies to:
2x = 4
Next, we divide both sides of the equation by 2:
(2x)/2 = 4/2
This simplifies to:
x = 2
Therefore, the unknown number is 2.
Solve for x.
3x−7−2x+5=6
3x−7−2x+5=6
To solve for x, we will combine like terms and isolate the variable on one side of the equation.
Starting with the given equation:
3x - 7 - 2x + 5 = 6
Combining like terms:
(3x - 2x) + (-7 + 5) = 6
x - 2 = 6
To isolate x, we need to move the constant term (-2) to the other side of the equation. We can do this by adding 2 to both sides:
(x - 2) + 2 = 6 + 2
x = 8
Therefore, the value of x is 8.
Starting with the given equation:
3x - 7 - 2x + 5 = 6
Combining like terms:
(3x - 2x) + (-7 + 5) = 6
x - 2 = 6
To isolate x, we need to move the constant term (-2) to the other side of the equation. We can do this by adding 2 to both sides:
(x - 2) + 2 = 6 + 2
x = 8
Therefore, the value of x is 8.
In Atlanta, the temperature was −2 °F in the morning in the winter. There was a winter storm, and the temperature dropped 10 degrees. What is the temperature now?(1 point)
To find the current temperature after the drop, we need to subtract 10 degrees from the initial temperature.
Starting with -2 °F, subtracting 10 degrees:
-2 °F - 10 = -12 °F
Therefore, the current temperature is -12 °F.
Starting with -2 °F, subtracting 10 degrees:
-2 °F - 10 = -12 °F
Therefore, the current temperature is -12 °F.
Shawn is solving the equation
x/7−47=−6
One of his steps is to multiply both sides of the equation by 7. Why?
(1 point)
Responses
Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
The negative sign in -6 must be changed to positive.
x/7−47=−6
One of his steps is to multiply both sides of the equation by 7. Why?
(1 point)
Responses
Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
The negative sign in -6 must be changed to positive.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.
A mountain climber starts a climb at an elevation of 380 ft. above sea level. At his first rest stop he has climbed 182 ft., and by his second rest stop he has climbed another 208 ft. It is getting late in the day, so the climber starts his way down the mountain. If the climber descends 235 ft, how much does he need to descend to return to his original starting point?(1 point)
To determine how much the climber needs to descend to return to his original starting point, we need to calculate the total elevation gained during the climb and subtract the descent.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
To return to the original starting point, the climber needs to descend 390 ft.
Therefore, the climber needs to descend 390 ft to return to his original starting point.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
To return to the original starting point, the climber needs to descend 390 ft.
Therefore, the climber needs to descend 390 ft to return to his original starting point.
A mountain climber starts a climb at an elevation of 380 ft. above sea level. At his first rest stop he has climbed 182 ft., and by his second rest stop he has climbed another 208 ft. It is getting late in the day, so the climber starts his way down the mountain. If the climber descends 235 ft, how much does he need to descend to return to his original starting point?(1 point)
Responses
155 feet
155 feet
78 feet
78 feet
535 feet
535 feet
235 feet
235 feet
Responses
155 feet
155 feet
78 feet
78 feet
535 feet
535 feet
235 feet
235 feet
To determine how much the climber needs to descend to return to his original starting point, we need to calculate the total elevation gained during the climb and subtract the descent.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
To return to the original starting point, the climber needs to descend an equal amount as the total elevation gained during the climb, which is 390 ft.
Therefore, the climber needs to descend 390 ft to return to his original starting point.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
To return to the original starting point, the climber needs to descend an equal amount as the total elevation gained during the climb, which is 390 ft.
Therefore, the climber needs to descend 390 ft to return to his original starting point.
out of the answer choices
out of the answer choices, the correct response is:
- 390 feet.
- 390 feet.
It is getting late in the day, so the climber starts his way down the mountain. If the climber descends 235 ft, how much does he need to descend to return to his original starting point?(1 point)
To determine how much the climber needs to descend to return to his original starting point, we need to calculate the total elevation gained during the climb and subtract the descent.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
Since the climber is descending, we subtract the descent of 235 ft from the total elevation gained:
390 ft - 235 ft = 155 ft
Therefore, the climber needs to descend 155 ft to return to his original starting point.
Starting at an elevation of 380 ft, the climber first climbs 182 ft, then an additional 208 ft, for a total elevation gained of 182 + 208 = 390 ft.
Since the climber is descending, we subtract the descent of 235 ft from the total elevation gained:
390 ft - 235 ft = 155 ft
Therefore, the climber needs to descend 155 ft to return to his original starting point.
Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, how much is the regular price of each ticket?(1 point)
To find the regular price of each ticket, we need to subtract the discount from the total cost and then divide by the number of tickets.
Let's assume x is the regular price of each ticket.
The discounted price is x - $1.50.
The total cost for 6 tickets is $51, so we can set up the equation:
6(x - $1.50) = $51
Expanding the left side of the equation:
6x - 6($1.50) = $51
6x - $9 = $51
To isolate x, we add $9 to both sides of the equation:
6x = $51 + $9
6x = $60
Finally, we divide both sides of the equation by 6:
x = $10
Therefore, the regular price of each ticket is $10.
Let's assume x is the regular price of each ticket.
The discounted price is x - $1.50.
The total cost for 6 tickets is $51, so we can set up the equation:
6(x - $1.50) = $51
Expanding the left side of the equation:
6x - 6($1.50) = $51
6x - $9 = $51
To isolate x, we add $9 to both sides of the equation:
6x = $51 + $9
6x = $60
Finally, we divide both sides of the equation by 6:
x = $10
Therefore, the regular price of each ticket is $10.
Which situation is best represented by the following equation?
12h+30=258(1 point)
Responses
Eric was paid $30 last week. He was paid a $258 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $30 last week. He was paid a $258 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $12 bonus and $30 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $12 bonus and $30 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $30 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $30 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $30 last week. He was paid a $12 bonus and $258 for each hour he worked. What is h, the number of hours Eric worked last week?
12h+30=258(1 point)
Responses
Eric was paid $30 last week. He was paid a $258 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $30 last week. He was paid a $258 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $12 bonus and $30 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $12 bonus and $30 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $30 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $30 bonus and $12 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $30 last week. He was paid a $12 bonus and $258 for each hour he worked. What is h, the number of hours Eric worked last week?
Eric was paid $258 last week. He was paid a $12 bonus and $30 for each hour he worked. What is h, the number of hours Eric worked last week?
Solve for x.
1/3(6x−9)=−33
1/3(6x−9)=−33
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
1/3(6x - 9) = -33
To eliminate the fraction, we can multiply both sides of the equation by 3:
3 * 1/3(6x - 9) = -33 * 3
This simplifies to:
(6x - 9) = -99
Next, we can add 9 to both sides of the equation to isolate the term with 6x:
(6x - 9) + 9 = -99 + 9
This simplifies to:
6x = -90
Finally, we can divide both sides of the equation by 6 to solve for x:
(6x)/6 = (-90)/6
This simplifies to:
x = -15
Therefore, the solution for x is -15.
Starting with the given equation:
1/3(6x - 9) = -33
To eliminate the fraction, we can multiply both sides of the equation by 3:
3 * 1/3(6x - 9) = -33 * 3
This simplifies to:
(6x - 9) = -99
Next, we can add 9 to both sides of the equation to isolate the term with 6x:
(6x - 9) + 9 = -99 + 9
This simplifies to:
6x = -90
Finally, we can divide both sides of the equation by 6 to solve for x:
(6x)/6 = (-90)/6
This simplifies to:
x = -15
Therefore, the solution for x is -15.
Solve for x.
−3/5(15x−30)=198
−3/5(15x−30)=198
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by 5/(-3):
(-3/5)(5/(-3))(15x - 30) = (5/(-3))(198)
Simplifying the left side of the equation:
15x - 30 = (-330/3)
Further simplifying:
15x - 30 = -110
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -110 + 30
This simplifies to:
15x = -80
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-80)/15
This simplifies to:
x = -80/15 or x = -16/3
Therefore, the solution for x is -16/3 or -5 and 1/3.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by 5/(-3):
(-3/5)(5/(-3))(15x - 30) = (5/(-3))(198)
Simplifying the left side of the equation:
15x - 30 = (-330/3)
Further simplifying:
15x - 30 = -110
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -110 + 30
This simplifies to:
15x = -80
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-80)/15
This simplifies to:
x = -80/15 or x = -16/3
Therefore, the solution for x is -16/3 or -5 and 1/3.
Solve for x.
−35(15x−30)=198 (1 point)
Responses
x = -24
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
−35(15x−30)=198 (1 point)
Responses
x = -24
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
-35(15x - 30) = 198
To get rid of the coefficient -35, we can divide both sides of the equation by -35:
-35(15x - 30)/-35 = 198/-35
Simplifying, we have:
15x - 30 = -198/35
Further simplifying the right side:
15x - 30 = -198/35
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -198/35 + 30
This simplifies to:
15x = -198/35 + 30
To add -198/35 and 30, we need a common denominator. The common denominator is 35, so:
15x = (-198 + 35*30)/35
Calculating the numerator:
15x = (-198 + 1050)/35
15x = 852/35
To simplify the fraction:
15x = 24.3428571429
Finally, divide both sides of the equation by 15 to solve for x:
(15x)/15 = 24.3428571429/15
This simplifies to:
x ≈ 1.623
Therefore, the approximate solution for x is 1.623.
Starting with the given equation:
-35(15x - 30) = 198
To get rid of the coefficient -35, we can divide both sides of the equation by -35:
-35(15x - 30)/-35 = 198/-35
Simplifying, we have:
15x - 30 = -198/35
Further simplifying the right side:
15x - 30 = -198/35
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -198/35 + 30
This simplifies to:
15x = -198/35 + 30
To add -198/35 and 30, we need a common denominator. The common denominator is 35, so:
15x = (-198 + 35*30)/35
Calculating the numerator:
15x = (-198 + 1050)/35
15x = 852/35
To simplify the fraction:
15x = 24.3428571429
Finally, divide both sides of the equation by 15 to solve for x:
(15x)/15 = 24.3428571429/15
This simplifies to:
x ≈ 1.623
Therefore, the approximate solution for x is 1.623.
Solve for x.
−3/5(15x−30)=198 (1 point)
Responses
x = -24
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
−3/5(15x−30)=198 (1 point)
Responses
x = -24
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by 5/(-3):
(-3/5)(5/(-3))(15x - 30) = (5/(-3))(198)
Simplifying the left side of the equation:
15x - 30 = (-330/3)
Further simplifying:
15x - 30 = -110
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -110 + 30
This simplifies to:
15x = -80
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-80)/15
This simplifies to:
x = -80/15 or x = -16/3
Therefore, the solution for x is -16/3 or -5 and 1/3.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by 5/(-3):
(-3/5)(5/(-3))(15x - 30) = (5/(-3))(198)
Simplifying the left side of the equation:
15x - 30 = (-330/3)
Further simplifying:
15x - 30 = -110
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -110 + 30
This simplifies to:
15x = -80
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-80)/15
This simplifies to:
x = -80/15 or x = -16/3
Therefore, the solution for x is -16/3 or -5 and 1/3.
which one
Looking at the provided options, the correct response would be:
x = -16/3
x = -16/3
x = -24
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
x = -24
x = -36
x = -36
x = -10
x = -10
x = -20
Apologies for the previous incorrect response.
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by -5/3:
(-5/3)(-3/5)(15x - 30) = (198)(-5/3)
Simplifying the left side of the equation:
15x - 30 = -660/3
Further simplifying:
15x - 30 = -220
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -220 + 30
This simplifies to:
15x = -190
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-190)/15
This simplifies to:
x = -190/15 or x = -38/3
Therefore, the solution for x is approximately -12.67 or -38/3. The option x = -24 is not a solution to the given equation.
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
-3/5(15x - 30) = 198
To eliminate the fraction, we can multiply both sides of the equation by -5/3:
(-5/3)(-3/5)(15x - 30) = (198)(-5/3)
Simplifying the left side of the equation:
15x - 30 = -660/3
Further simplifying:
15x - 30 = -220
Next, we add 30 to both sides of the equation to isolate the term with 15x:
15x - 30 + 30 = -220 + 30
This simplifies to:
15x = -190
Finally, we divide both sides of the equation by 15 to solve for x:
(15x)/15 = (-190)/15
This simplifies to:
x = -190/15 or x = -38/3
Therefore, the solution for x is approximately -12.67 or -38/3. The option x = -24 is not a solution to the given equation.
Solve for x.
3(4x−12)=84 (1 point)
3(4x−12)=84 (1 point)
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
3(4x - 12) = 84
First, we can distribute 3 to the terms inside the parentheses:
12x - 36 = 84
Next, we can add 36 to both sides of the equation to isolate the term with 12x:
12x - 36 + 36 = 84 + 36
This simplifies to:
12x = 120
Finally, we divide both sides of the equation by 12 to solve for x:
(12x)/12 = 120/12
This simplifies to:
x = 10
Therefore, the solution for x is 10.
Starting with the given equation:
3(4x - 12) = 84
First, we can distribute 3 to the terms inside the parentheses:
12x - 36 = 84
Next, we can add 36 to both sides of the equation to isolate the term with 12x:
12x - 36 + 36 = 84 + 36
This simplifies to:
12x = 120
Finally, we divide both sides of the equation by 12 to solve for x:
(12x)/12 = 120/12
This simplifies to:
x = 10
Therefore, the solution for x is 10.
Solve for x.
20(2x−8)=440
20(2x−8)=440
To solve for x, we will isolate the variable on one side of the equation.
Starting with the given equation:
20(2x - 8) = 440
First, we can distribute 20 to the terms inside the parentheses:
40x - 160 = 440
Next, we can add 160 to both sides of the equation to isolate the term with 40x:
40x - 160 + 160 = 440 + 160
This simplifies to:
40x = 600
Finally, we divide both sides of the equation by 40 to solve for x:
(40x)/40 = 600/40
This simplifies to:
x = 15
Therefore, the solution for x is 15.
Starting with the given equation:
20(2x - 8) = 440
First, we can distribute 20 to the terms inside the parentheses:
40x - 160 = 440
Next, we can add 160 to both sides of the equation to isolate the term with 40x:
40x - 160 + 160 = 440 + 160
This simplifies to:
40x = 600
Finally, we divide both sides of the equation by 40 to solve for x:
(40x)/40 = 600/40
This simplifies to:
x = 15
Therefore, the solution for x is 15.
Solve for x.
0.72=0.4(x+1.4)
0.72=0.4(x+1.4)
To solve for x, we'll isolate the variable on one side of the equation.
Starting with the given equation:
0.72 = 0.4(x + 1.4)
First, we can simplify the expression on the right side of the equation:
0.72 = 0.4x + 0.56
Next, we can subtract 0.56 from both sides of the equation to isolate the term with 0.4x:
0.72 - 0.56 = 0.4x
This simplifies to:
0.16 = 0.4x
Finally, we divide both sides of the equation by 0.4 to solve for x:
0.16 / 0.4 = x
This simplifies to:
0.4 = x
Therefore, the solution for x is 0.4.
Starting with the given equation:
0.72 = 0.4(x + 1.4)
First, we can simplify the expression on the right side of the equation:
0.72 = 0.4x + 0.56
Next, we can subtract 0.56 from both sides of the equation to isolate the term with 0.4x:
0.72 - 0.56 = 0.4x
This simplifies to:
0.16 = 0.4x
Finally, we divide both sides of the equation by 0.4 to solve for x:
0.16 / 0.4 = x
This simplifies to:
0.4 = x
Therefore, the solution for x is 0.4.
Solve for x.
2(1.5x−7)=6
2(1.5x−7)=6
To solve for x, we will isolate the variable
step by step