To solve for x, we can divide both sides of the equation by -5:
(-5x)/-5 = (-30)/-5
Simplifying, we have:
x = 6
Solve for x.
−5x=−30
29 answers
Solve for x.
12−x/9=11
12−x/9=11
To solve for x, we will first eliminate the fraction by multiplying both sides of the equation by 9:
9 * (12 - x)/9 = 11 * 9
Simplifying, we have:
12 - x = 99
Next, isolate x by subtracting 12 from both sides:
12 - x - 12 = 99 - 12
Simplifying, we have:
-x = 87
Finally, multiply both sides of the equation by -1 to solve for x:
(-1) * (-x) = (-1) * 87
Simplifying, we have:
x = -87
9 * (12 - x)/9 = 11 * 9
Simplifying, we have:
12 - x = 99
Next, isolate x by subtracting 12 from both sides:
12 - x - 12 = 99 - 12
Simplifying, we have:
-x = 87
Finally, multiply both sides of the equation by -1 to solve for x:
(-1) * (-x) = (-1) * 87
Simplifying, we have:
x = -87
Solve for x.
−20=−5+3x
−20=−5+3x
To solve for x, we will isolate the variable x by moving all the terms without x to one side of the equation.
Starting with the given equation:
-20 = -5 + 3x
We can begin by subtracting -5 from both sides to eliminate the term:
-20 - (-5) = -5 + 3x - (-5)
Simplifying, we have:
-20 + 5 = 3x
-15 = 3x
Next, to isolate x, divide both sides of the equation by 3:
(-15)/3 = 3x/3
Simplifying, we have:
-5 = x
Therefore, x equals -5.
Starting with the given equation:
-20 = -5 + 3x
We can begin by subtracting -5 from both sides to eliminate the term:
-20 - (-5) = -5 + 3x - (-5)
Simplifying, we have:
-20 + 5 = 3x
-15 = 3x
Next, to isolate x, divide both sides of the equation by 3:
(-15)/3 = 3x/3
Simplifying, we have:
-5 = x
Therefore, x equals -5.
Solve for x.
7(4x−15)=63
7(4x−15)=63
To solve for x, we will first simplify the equation by distributing 7 to each term inside the parentheses:
7(4x - 15) = 63
28x - 105 = 63
Next, we will isolate the term with x on one side by adding 105 to both sides of the equation:
28x - 105 + 105 = 63 + 105
Simplifying, we have:
28x = 168
Finally, we can solve for x by dividing both sides of the equation by 28:
28x/28 = 168/28
Simplifying, we have:
x = 6
Therefore, x equals 6.
7(4x - 15) = 63
28x - 105 = 63
Next, we will isolate the term with x on one side by adding 105 to both sides of the equation:
28x - 105 + 105 = 63 + 105
Simplifying, we have:
28x = 168
Finally, we can solve for x by dividing both sides of the equation by 28:
28x/28 = 168/28
Simplifying, we have:
x = 6
Therefore, x equals 6.
Solve for x: −2(3x−15)−25=35.
To solve for x, we will first simplify the equation using the distributive property and combining like terms:
-2(3x - 15) - 25 = 35
Distribute -2 to both terms within the parentheses:
-6x + 30 - 25 = 35
Combine like terms:
-6x + 5 = 35
Next, isolate the x-term by subtracting 5 from both sides:
-6x + 5 - 5 = 35 - 5
Simplifying, we have:
-6x = 30
Finally, solve for x by dividing both sides of the equation by -6:
(-6x)/-6 = 30/-6
Simplifying, we have:
x = -5
Therefore, x equals -5.
-2(3x - 15) - 25 = 35
Distribute -2 to both terms within the parentheses:
-6x + 30 - 25 = 35
Combine like terms:
-6x + 5 = 35
Next, isolate the x-term by subtracting 5 from both sides:
-6x + 5 - 5 = 35 - 5
Simplifying, we have:
-6x = 30
Finally, solve for x by dividing both sides of the equation by -6:
(-6x)/-6 = 30/-6
Simplifying, we have:
x = -5
Therefore, x equals -5.
Solve for x: 12x+5=10x−11
To solve for x, we will isolate the x-term on one side of the equation by moving all other terms to the opposite side.
Starting with the given equation:
12x + 5 = 10x - 11
We can begin by subtracting 10x from both sides to eliminate the x-term on the right side:
12x + 5 - 10x = 10x - 11 - 10x
Simplifying, we have:
2x + 5 = -11
Next, we will subtract 5 from both sides to move the constant term to the other side:
2x + 5 - 5 = -11 - 5
Simplifying, we have:
2x = -16
Finally, divide both sides of the equation by 2 to solve for x:
(2x)/2 = (-16)/2
Simplifying, we have:
x = -8
Therefore, x equals -8.
Starting with the given equation:
12x + 5 = 10x - 11
We can begin by subtracting 10x from both sides to eliminate the x-term on the right side:
12x + 5 - 10x = 10x - 11 - 10x
Simplifying, we have:
2x + 5 = -11
Next, we will subtract 5 from both sides to move the constant term to the other side:
2x + 5 - 5 = -11 - 5
Simplifying, we have:
2x = -16
Finally, divide both sides of the equation by 2 to solve for x:
(2x)/2 = (-16)/2
Simplifying, we have:
x = -8
Therefore, x equals -8.
At the beginning of the month, a song on a streaming service already had 1,000 listens, and was getting 38 new listens each day. Meanwhile, a different song already had 900 listens, and was getting 40 new listens each day. Write an equation to show the number of days it would take for the two songs to have the same number of listens. Use x as your variable.
To find the number of days it would take for the two songs to have the same number of listens, we can set up an equation:
1,000 + 38x = 900 + 40x
In this equation, x represents the number of days.
The left side represents the total number of listens for the first song, starting with 1,000 and increasing by 38 listens each day. The right side represents the total number of listens for the second song, starting with 900 and increasing by 40 listens each day.
Simplifying the equation, we have:
38x - 40x = 900 - 1000
-2x = -100
Dividing both sides of the equation by -2, we find:
x = 50
Therefore, it would take 50 days for the two songs to have the same number of listens.
1,000 + 38x = 900 + 40x
In this equation, x represents the number of days.
The left side represents the total number of listens for the first song, starting with 1,000 and increasing by 38 listens each day. The right side represents the total number of listens for the second song, starting with 900 and increasing by 40 listens each day.
Simplifying the equation, we have:
38x - 40x = 900 - 1000
-2x = -100
Dividing both sides of the equation by -2, we find:
x = 50
Therefore, it would take 50 days for the two songs to have the same number of listens.
An ice skating rink has two ways you can use the facility. The first option is to pay $10 per visit. The second option is to pay $32 per month, and $6 per visit. Write and solve an equation to show the number of visits it would take for the cost of the two plans to be equal.
To find the number of visits it would take for the cost of the two plans to be equal, we can set up an equation.
Let's use v to represent the number of visits.
For the first option, the cost is $10 per visit, so the equation would be:
10v
For the second option, the cost is $32 per month plus $6 per visit. If we assume a month has 30 days, then the equation would be:
32 + 6v
To find the number of visits that would make these two costs equal, we can set up the equation:
10v = 32 + 6v
To solve for v, we begin by subtracting 6v from both sides of the equation:
10v - 6v = 32
Simplifying, we have:
4v = 32
Next, we divide both sides of the equation by 4:
4v/4 = 32/4
Simplifying, we have:
v = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
Let's use v to represent the number of visits.
For the first option, the cost is $10 per visit, so the equation would be:
10v
For the second option, the cost is $32 per month plus $6 per visit. If we assume a month has 30 days, then the equation would be:
32 + 6v
To find the number of visits that would make these two costs equal, we can set up the equation:
10v = 32 + 6v
To solve for v, we begin by subtracting 6v from both sides of the equation:
10v - 6v = 32
Simplifying, we have:
4v = 32
Next, we divide both sides of the equation by 4:
4v/4 = 32/4
Simplifying, we have:
v = 8
Therefore, it would take 8 visits for the cost of the two plans to be equal.
At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens?(1 point)
The songs will have the same number of listens after
days.
The songs will have the same number of listens after
days.
Let's use x as the number of days it takes for the two songs to have the same number of listens.
For the first song, starting with 700 listens and increasing by 52 listens each day, the total number of listens after x days can be represented by the equation: 700 + 52x.
For the second song, starting with 600 listens and increasing by 56 listens each day, the total number of listens after x days can be represented by the equation: 600 + 56x.
To find when the two songs have the same number of listens, we can set up the equation:
700 + 52x = 600 + 56x
To solve for x, we need to isolate the x term. Let's subtract 52x from both sides:
700 = 600 + 56x - 52x
700 = 600 + 4x
Next, subtract 600 from both sides:
700 - 600 = 600 - 600 + 4x
100 = 4x
Finally, divide both sides of the equation by 4 to solve for x:
100 / 4 = 4x / 4
25 = x
Therefore, the songs will have the same number of listens after 25 days.
For the first song, starting with 700 listens and increasing by 52 listens each day, the total number of listens after x days can be represented by the equation: 700 + 52x.
For the second song, starting with 600 listens and increasing by 56 listens each day, the total number of listens after x days can be represented by the equation: 600 + 56x.
To find when the two songs have the same number of listens, we can set up the equation:
700 + 52x = 600 + 56x
To solve for x, we need to isolate the x term. Let's subtract 52x from both sides:
700 = 600 + 56x - 52x
700 = 600 + 4x
Next, subtract 600 from both sides:
700 - 600 = 600 - 600 + 4x
100 = 4x
Finally, divide both sides of the equation by 4 to solve for x:
100 / 4 = 4x / 4
25 = x
Therefore, the songs will have the same number of listens after 25 days.
Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?
To determine when Miguel and Christina will have the same amount of gas in their tanks, we first need to find the number of weeks it will take for them to use up their respective gas capacities.
For Miguel's car with a 20-gallon capacity, dividing the total capacity by the amount consumed weekly (1.5 gallons) yields:
20 gallons / 1.5 gallons/week = 13.33 weeks (approximately)
For Christina's car with a 16-gallon capacity, dividing the total capacity by the amount consumed weekly (1 gallon) gives:
16 gallons / 1 gallon/week = 16 weeks
To find when they will have the same amount of gas, we need to find a common multiple of both 13.33 and 16.
The least common multiple (LCM) of 13.33 and 16 is:
LCM(13.33, 16) = 53.32 (approximately)
Thus, it will take them around 53.32 weeks to have the same amount of gas in their tanks.
Please note that this approximation assumes that their gas consumption remains constant over time.
For Miguel's car with a 20-gallon capacity, dividing the total capacity by the amount consumed weekly (1.5 gallons) yields:
20 gallons / 1.5 gallons/week = 13.33 weeks (approximately)
For Christina's car with a 16-gallon capacity, dividing the total capacity by the amount consumed weekly (1 gallon) gives:
16 gallons / 1 gallon/week = 16 weeks
To find when they will have the same amount of gas, we need to find a common multiple of both 13.33 and 16.
The least common multiple (LCM) of 13.33 and 16 is:
LCM(13.33, 16) = 53.32 (approximately)
Thus, it will take them around 53.32 weeks to have the same amount of gas in their tanks.
Please note that this approximation assumes that their gas consumption remains constant over time.
Miguel’s car has a 20-gallon capacity, and Christina’s car has a 16-gallon capacity. Miguel uses 1.5 gallons of gas per week, and Christina uses 1 gallon of gas per week. When will Miguel and Christina have the same amount of gas in their tanks?(1 point)
Responses
After 1.6 weeks they will have the same amount of gas in their tanks.
After 1.6 weeks they will have the same amount of gas in their tanks.
After −8 weeks they will have the same amount of gas in their tanks.
After negative 8 weeks they will have the same amount of gas in their tanks.
After 18 week they will have the same amount of gas in their tanks.
After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks.
After 8 weeks they will have the same amount of gas in their tanks.
Responses
After 1.6 weeks they will have the same amount of gas in their tanks.
After 1.6 weeks they will have the same amount of gas in their tanks.
After −8 weeks they will have the same amount of gas in their tanks.
After negative 8 weeks they will have the same amount of gas in their tanks.
After 18 week they will have the same amount of gas in their tanks.
After Start Fraction 1 over 8 End Fraction week they will have the same amount of gas in their tanks.
After 8 weeks they will have the same amount of gas in their tanks.
To determine when Miguel and Christina will have the same amount of gas in their tanks, we can set up an equation:
1.5x + 20 = 1x + 16
Where x represents the number of weeks.
Simplifying the equation, we have:
0.5x = -4
Now, let's solve for x by dividing both sides of the equation by 0.5:
0.5x / 0.5 = -4 / 0.5
x = -8
The solution for x is -8. This means that after 8 weeks, Miguel and Christina will have the same amount of gas in their tanks. Please note that the negative sign in front of 8 indicates that this is the number of weeks in the past when their gas levels were equal.
1.5x + 20 = 1x + 16
Where x represents the number of weeks.
Simplifying the equation, we have:
0.5x = -4
Now, let's solve for x by dividing both sides of the equation by 0.5:
0.5x / 0.5 = -4 / 0.5
x = -8
The solution for x is -8. This means that after 8 weeks, Miguel and Christina will have the same amount of gas in their tanks. Please note that the negative sign in front of 8 indicates that this is the number of weeks in the past when their gas levels were equal.
Solving Linear Equations Unit Test
12 of 1512 of 15 Items
Question
Which of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−3x−8=3x−8
12 of 1512 of 15 Items
Question
Which of the following equations has exactly one solution?(1 point)
Responses
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
−8x+3=−8x+3
negative 8 x plus 3 equals negative 8 x plus 3
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−3x−8=3x−8
The equation that has exactly one solution is −3x+8=−3x−8.
Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
11x=3(7x−1)−10x(1 point)
Responses
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
To determine the number of solutions for the equation 11x = 3(7x - 1) - 10x, we will start by simplifying both sides of the equation:
11x = 21x - 3 - 10x
Next, we will combine like terms on the right side:
11x = 11x - 3
Now, we have the same term on both sides of the equation. However, when we subtract 11x from both sides, we will eliminate x from the equation:
0 = -3
Since this equation results in a contradiction (0 is not equal to -3), we can conclude that there is no solution for the equation.
Therefore, the correct response is: The equation has no solution.
11x = 21x - 3 - 10x
Next, we will combine like terms on the right side:
11x = 11x - 3
Now, we have the same term on both sides of the equation. However, when we subtract 11x from both sides, we will eliminate x from the equation:
0 = -3
Since this equation results in a contradiction (0 is not equal to -3), we can conclude that there is no solution for the equation.
Therefore, the correct response is: The equation has no solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−4=2x+6(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions
5(2x+2)−4=2x+6(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=1.
The equation has one solution: x equals 1 .
The equation has infinite solutions
To determine the number of solutions for the equation 5(2x+2) − 4 = 2x + 6, we will start by simplifying both sides of the equation:
10x + 10 - 4 = 2x + 6
Next, we will combine like terms on both sides of the equation:
10x + 6 = 2x + 6
Now, we will subtract 2x from both sides to isolate the x term:
10x - 2x + 6 = 2x - 2x + 6
Combining like terms again:
8x + 6 = 6
Next, we will subtract 6 from both sides:
8x + 6 - 6 = 6 - 6
Simplifying:
8x = 0
Finally, to solve for x, we will divide both sides of the equation by 8:
(8x)/8 = 0/8
Simplifying:
x = 0
Therefore, the correct response is: The equation has one solution: x = 0.
10x + 10 - 4 = 2x + 6
Next, we will combine like terms on both sides of the equation:
10x + 6 = 2x + 6
Now, we will subtract 2x from both sides to isolate the x term:
10x - 2x + 6 = 2x - 2x + 6
Combining like terms again:
8x + 6 = 6
Next, we will subtract 6 from both sides:
8x + 6 - 6 = 6 - 6
Simplifying:
8x = 0
Finally, to solve for x, we will divide both sides of the equation by 8:
(8x)/8 = 0/8
Simplifying:
x = 0
Therefore, the correct response is: The equation has one solution: x = 0.
Solve the following linear equation for x. Then check your answer. Show all your steps for solving and checking.
5x+8+x=32
(4 points)
5x+8+x=32
(4 points)
To solve the equation 5x + 8 + x = 32, we will combine like terms and isolate the x term.
First, we combine 5x and x:
6x + 8 = 32
Next, we subtract 8 from both sides to isolate the x term on one side:
6x + 8 - 8 = 32 - 8
Simplifying, we have:
6x = 24
To solve for x, we divide both sides of the equation by 6:
(6x) / 6 = 24 / 6
Simplifying, we have:
x = 4
So, the solution to the equation is x = 4.
To check the solution, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
Simplifying the equation, we have:
20 + 8 + 4 = 32
32 = 32
The left side of the equation is equal to the right side, so the solution x = 4 is verified as correct.
First, we combine 5x and x:
6x + 8 = 32
Next, we subtract 8 from both sides to isolate the x term on one side:
6x + 8 - 8 = 32 - 8
Simplifying, we have:
6x = 24
To solve for x, we divide both sides of the equation by 6:
(6x) / 6 = 24 / 6
Simplifying, we have:
x = 4
So, the solution to the equation is x = 4.
To check the solution, we substitute x = 4 back into the original equation:
5(4) + 8 + 4 = 32
Simplifying the equation, we have:
20 + 8 + 4 = 32
32 = 32
The left side of the equation is equal to the right side, so the solution x = 4 is verified as correct.
1 answer