To solve for x, we need to isolate x on one side of the equation.
Starting with -5x = -30, we can divide both sides of the equation by -5 to get rid of the coefficient in front of x.
(-5x) / -5 = (-30) / -5
This simplifies to:
x = 6
Solve for x .
−5x=−30 (1 point)
29 answers
Solve for x .
12−x9=11 (1 point)
12−x9=11 (1 point)
To solve for x, we need to isolate x on one side of the equation.
Starting with 12 - (x/9) = 11, we can subtract 12 from both sides of the equation to get rid of the constant on the left side.
12 - 12 - (x/9) = 11 - 12
This simplifies to:
-x/9 = -1
To eliminate the fraction, we can multiply both sides of the equation by 9:
9 * (-x/9) = 9 * (-1)
This simplifies to:
-x = -9
To solve for x, we can multiply both sides of the equation by -1 to get rid of the negative sign:
(-1) * (-x) = (-1) * (-9)
This simplifies to:
x = 9
Starting with 12 - (x/9) = 11, we can subtract 12 from both sides of the equation to get rid of the constant on the left side.
12 - 12 - (x/9) = 11 - 12
This simplifies to:
-x/9 = -1
To eliminate the fraction, we can multiply both sides of the equation by 9:
9 * (-x/9) = 9 * (-1)
This simplifies to:
-x = -9
To solve for x, we can multiply both sides of the equation by -1 to get rid of the negative sign:
(-1) * (-x) = (-1) * (-9)
This simplifies to:
x = 9
Solve for x .
−20=−5+3x (1 point)
−20=−5+3x (1 point)
To solve for x, we need to isolate x on one side of the equation.
Starting with -20 = -5 + 3x, we can subtract -5 from both sides of the equation to get rid of the constant term on the right side.
-20 - (-5) = -5 + 3x - (-5)
This simplifies to:
-20 + 5 = 3x
Combine like terms:
-15 = 3x
To solve for x, we can divide both sides of the equation by 3:
(-15) / 3 = (3x) / 3
This simplifies to:
-5 = x
So the solution is x = -5.
Starting with -20 = -5 + 3x, we can subtract -5 from both sides of the equation to get rid of the constant term on the right side.
-20 - (-5) = -5 + 3x - (-5)
This simplifies to:
-20 + 5 = 3x
Combine like terms:
-15 = 3x
To solve for x, we can divide both sides of the equation by 3:
(-15) / 3 = (3x) / 3
This simplifies to:
-5 = x
So the solution is x = -5.
Solve for x .
20=5−38x (1 point)
20=5−38x (1 point)
To solve for x, we need to isolate x on one side of the equation.
Starting with 20 = 5 - 38x, we can add 38x to both sides to get rid of the term with x.
20 + 38x = 5 - 38x + 38x
This simplifies to:
38x + 38x = 5 + 20
Combine like terms:
76x = 25
To solve for x, we can divide both sides of the equation by 76:
(76x) / 76 = (25) / 76
This simplifies to:
x = 25/76
So the solution is x = 25/76.
Starting with 20 = 5 - 38x, we can add 38x to both sides to get rid of the term with x.
20 + 38x = 5 - 38x + 38x
This simplifies to:
38x + 38x = 5 + 20
Combine like terms:
76x = 25
To solve for x, we can divide both sides of the equation by 76:
(76x) / 76 = (25) / 76
This simplifies to:
x = 25/76
So the solution is x = 25/76.
Solve for x .
7(4x−15)=63
7(4x−15)=63
To solve for x, we need to isolate x on one side of the equation.
Starting with 7(4x - 15) = 63, we can distribute the 7 on the left side of the equation.
28x - 105 = 63
Next, we can add 105 to both sides of the equation to get rid of the constant term on the left side.
28x - 105 + 105 = 63 + 105
This simplifies to:
28x = 168
To solve for x, we can divide both sides of the equation by 28:
(28x) / 28 = (168) / 28
This simplifies to:
x = 6
So the solution is x = 6.
Starting with 7(4x - 15) = 63, we can distribute the 7 on the left side of the equation.
28x - 105 = 63
Next, we can add 105 to both sides of the equation to get rid of the constant term on the left side.
28x - 105 + 105 = 63 + 105
This simplifies to:
28x = 168
To solve for x, we can divide both sides of the equation by 28:
(28x) / 28 = (168) / 28
This simplifies to:
x = 6
So the solution is x = 6.
Solve for x : −2(3x−15)−25=35 .(1 point)
To solve for x, we need to isolate x on one side of the equation.
Starting with -2(3x - 15) - 25 = 35, we can first distribute the -2 on the left side of the equation.
-6x + 30 - 25 = 35
Combine like terms:
-6x + 5 = 35
Next, we can subtract 5 from both sides of the equation to get rid of the constant term on the left side.
-6x + 5 - 5 = 35 - 5
This simplifies to:
-6x = 30
To solve for x, we can divide both sides of the equation by -6:
(-6x) / -6 = (30) / -6
This simplifies to:
x = -5
So the solution is x = -5.
Starting with -2(3x - 15) - 25 = 35, we can first distribute the -2 on the left side of the equation.
-6x + 30 - 25 = 35
Combine like terms:
-6x + 5 = 35
Next, we can subtract 5 from both sides of the equation to get rid of the constant term on the left side.
-6x + 5 - 5 = 35 - 5
This simplifies to:
-6x = 30
To solve for x, we can divide both sides of the equation by -6:
(-6x) / -6 = (30) / -6
This simplifies to:
x = -5
So the solution is x = -5.
Solve for x : 12x+5=10x−11 .(1 point)
To solve for x, we need to isolate x on one side of the equation.
Starting with 12x + 5 = 10x - 11, we can start by subtracting 10x from both sides of the equation.
12x - 10x + 5 = 10x - 10x - 11
This simplifies to:
2x + 5 = -11
Next, we can subtract 5 from both sides of the equation to get rid of the constant term on the left side.
2x + 5 - 5 = -11 - 5
This simplifies to:
2x = -16
To solve for x, we can divide both sides of the equation by 2:
(2x) / 2 = (-16) / 2
This simplifies to:
x = -8
So the solution is x = -8.
Starting with 12x + 5 = 10x - 11, we can start by subtracting 10x from both sides of the equation.
12x - 10x + 5 = 10x - 10x - 11
This simplifies to:
2x + 5 = -11
Next, we can subtract 5 from both sides of the equation to get rid of the constant term on the left side.
2x + 5 - 5 = -11 - 5
This simplifies to:
2x = -16
To solve for x, we can divide both sides of the equation by 2:
(2x) / 2 = (-16) / 2
This simplifies to:
x = -8
So the solution is x = -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.(1 point)
Let's denote the number of days as x.
For the first song, the total number of listens after x days would be 1000 + 38x.
For the second song, the total number of listens after x days would be 900 + 40x.
To find the number of days it would take for the two songs to have the same number of listens, we set up the equation:
1000 + 38x = 900 + 40x
For the first song, the total number of listens after x days would be 1000 + 38x.
For the second song, the total number of listens after x days would be 900 + 40x.
To find the number of days it would take for the two songs to have the same number of listens, we set up the equation:
1000 + 38x = 900 + 40x
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.(1 point)
Responses
10x=32+6x ; x=4
10 x equals 32 plus 6 x ; x equals 4
10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3
10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2
10x=32+6x ; x=8
Responses
10x=32+6x ; x=4
10 x equals 32 plus 6 x ; x equals 4
10=32+6x ; x=−3
10 equals 32 plus 6 x ; x equals negative 3
10x=32−6x ; x=2
10 x equals 32 minus 6 x ; x equals 2
10x=32+6x ; x=8
To find the number of visits it would take for the cost of the two plans to be equal, we set up the equation:
10x = 32 + 6x
To solve for x, we want to isolate the x term on one side of the equation. We can do this by subtracting 6x from both sides:
10x - 6x = 32 + 6x - 6x
This simplifies to:
4x = 32
To solve for x, we can divide both sides of the equation by 4:
(4x) / 4 = (32) / 4
This simplifies to:
x = 8
So it would take 8 visits for the cost of the two plans to be equal.
10x = 32 + 6x
To solve for x, we want to isolate the x term on one side of the equation. We can do this by subtracting 6x from both sides:
10x - 6x = 32 + 6x - 6x
This simplifies to:
4x = 32
To solve for x, we can divide both sides of the equation by 4:
(4x) / 4 = (32) / 4
This simplifies to:
x = 8
So 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.
To find the number of days it will take for the two songs to have the same number of listens, we can set up an equation.
Let's use 'x' to represent the number of days.
For the first song, the total number of listens after x days would be 700 + 52x.
For the second song, the total number of listens after x days would be 600 + 56x.
To find when the two songs have the same number of listens, we set up the equation:
700 + 52x = 600 + 56x
To solve for x, we want to isolate the x term on one side of the equation. We can do this by subtracting 52x from both sides:
700 + 52x - 52x = 600 + 56x - 52x
This simplifies to:
700 = 600 + 4x
Next, we subtract 600 from both sides:
700 - 600 = 600 + 4x - 600
This simplifies to:
100 = 4x
To solve for x, we can divide both sides of the equation by 4:
(100) / 4 = (4x) / 4
This simplifies to:
25 = x
Therefore, it will take 25 days for the two songs to have the same number of listens.
Let's use 'x' to represent the number of days.
For the first song, the total number of listens after x days would be 700 + 52x.
For the second song, the total number of listens after x days would be 600 + 56x.
To find when the two songs have the same number of listens, we set up the equation:
700 + 52x = 600 + 56x
To solve for x, we want to isolate the x term on one side of the equation. We can do this by subtracting 52x from both sides:
700 + 52x - 52x = 600 + 56x - 52x
This simplifies to:
700 = 600 + 4x
Next, we subtract 600 from both sides:
700 - 600 = 600 + 4x - 600
This simplifies to:
100 = 4x
To solve for x, we can divide both sides of the equation by 4:
(100) / 4 = (4x) / 4
This simplifies to:
25 = x
Therefore, it will take 25 days for the two songs to have the same number of listens.
Which of the following equations has no solutions?(1 point)
Responses
6x+4=6x+4
6 x plus 4 equals 6 x plus 4
6x+3=−6x+3
6 x plus 3 equals negative 6 x plus 3
−6x+4=−6x+3
negative 6 x plus 4 equals negative 6 x plus 3
−6x+4=6x+3
Responses
6x+4=6x+4
6 x plus 4 equals 6 x plus 4
6x+3=−6x+3
6 x plus 3 equals negative 6 x plus 3
−6x+4=−6x+3
negative 6 x plus 4 equals negative 6 x plus 3
−6x+4=6x+3
The equation that has no solutions is:
−6x + 4 = 6x + 3
In this equation, if we simplify it, we will end up with:
−6x + 4 - 6x - 3 = 0
Combining like terms gives us:
-12x + 1 = 0
We cannot solve for x from this equation since the variable x is eliminated from the equation and we are left with a contradiction. Therefore, there are no values of x that satisfy this equation, and it has no solutions.
−6x + 4 = 6x + 3
In this equation, if we simplify it, we will end up with:
−6x + 4 - 6x - 3 = 0
Combining like terms gives us:
-12x + 1 = 0
We cannot solve for x from this equation since the variable x is eliminated from the equation and we are left with a contradiction. Therefore, there are no values of x that satisfy this equation, and it has no solutions.
Which of the following equations has exactly one solution?(1 point)
Responses
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
Responses
−3x−8=3x−8
negative 3 x minus 8 equals 3 x minus 8
−3x+8=−3x−8
negative 3 x plus 8 equals negative 3 x minus 8
3x−8=3x+8
3 x minus 8 equals 3 x plus 8
−8x+3=−8x+3
The equation that has exactly one solution is:
−3x − 8 = 3x − 8
In this equation, if we simplify it, we will end up with:
−3x − 8 − 3x + 8 = 0
Combine like terms:
-6x = 0
To solve for x, we can divide both sides of the equation by -6:
(-6x) / -6 = 0 / -6
This simplifies to:
x = 0
Therefore, the equation −3x − 8 = 3x − 8 has exactly one solution, which is x = 0.
−3x − 8 = 3x − 8
In this equation, if we simplify it, we will end up with:
−3x − 8 − 3x + 8 = 0
Combine like terms:
-6x = 0
To solve for x, we can divide both sides of the equation by -6:
(-6x) / -6 = 0 / -6
This simplifies to:
x = 0
Therefore, the equation −3x − 8 = 3x − 8 has exactly one solution, which is x = 0.
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 one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
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 one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
To determine if the equation has one, none, or infinite solutions, we need to simplify both sides of the equation and then solve for x.
Starting with 11x = 3(7x - 1) - 10x, we can start by distributing the 3 on the right side of the equation:
11x = 21x - 3 - 10x
Combine like terms:
11x - 21x + 10x = -3
Simplify:
0 = -3
Since 0 is not equal to -3, we have a contradiction. Therefore, the equation has no solution.
So, the correct response is:
The equation has no solution.
Starting with 11x = 3(7x - 1) - 10x, we can start by distributing the 3 on the right side of the equation:
11x = 21x - 3 - 10x
Combine like terms:
11x - 21x + 10x = -3
Simplify:
0 = -3
Since 0 is not equal to -3, we have a contradiction. Therefore, the equation has no solution.
So, 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 infinite solutions.
The equation has infinite solutions.
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 no solution.
5(2x+2)−4=2x+6 (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
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 no solution.
To determine if the equation has one, none, or infinite solutions, we need to simplify both sides of the equation and then solve for x.
Starting with 5(2x + 2) - 4 = 2x + 6, we can start by simplifying the left side of the equation:
10x + 10 - 4 = 2x + 6
Combine like terms:
10x + 6 = 2x + 6
Next, we want to isolate x on one side of the equation. We can do this by subtracting 2x from both sides:
10x - 2x + 6 = 2x - 2x + 6
Simplify:
8x + 6 = 6
Next, we subtract 6 from both sides:
8x + 6 - 6 = 6 - 6
Simplify:
8x = 0
To solve for x, we can divide both sides of the equation by 8:
(8x) / 8 = 0 / 8
Simplify:
x = 0
Therefore, the equation has one solution: x = 0.
So the correct response is:
The equation has one solution: x = 0.
Starting with 5(2x + 2) - 4 = 2x + 6, we can start by simplifying the left side of the equation:
10x + 10 - 4 = 2x + 6
Combine like terms:
10x + 6 = 2x + 6
Next, we want to isolate x on one side of the equation. We can do this by subtracting 2x from both sides:
10x - 2x + 6 = 2x - 2x + 6
Simplify:
8x + 6 = 6
Next, we subtract 6 from both sides:
8x + 6 - 6 = 6 - 6
Simplify:
8x = 0
To solve for x, we can divide both sides of the equation by 8:
(8x) / 8 = 0 / 8
Simplify:
x = 0
Therefore, the equation has one solution: x = 0.
So 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 for x, we can start by combining like terms on the left side:
6x + 8 = 32
Next, we want to isolate x on one side of the equation. We can do this by subtracting 8 from both sides:
6x + 8 - 8 = 32 - 8
This simplifies to:
6x = 24
To solve for x, we can divide both sides of the equation by 6:
(6x) / 6 = 24 / 6
This simplifies to:
x = 4
Now, let's check our answer by substituting x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
Therefore, the solution to the equation 5x + 8 + x = 32 is x = 4.
6x + 8 = 32
Next, we want to isolate x on one side of the equation. We can do this by subtracting 8 from both sides:
6x + 8 - 8 = 32 - 8
This simplifies to:
6x = 24
To solve for x, we can divide both sides of the equation by 6:
(6x) / 6 = 24 / 6
This simplifies to:
x = 4
Now, let's check our answer by substituting x = 4 back into the original equation:
5(4) + 8 + 4 = 32
20 + 8 + 4 = 32
32 = 32
Since both sides of the equation are equal, our solution x = 4 is correct.
Therefore, the solution to the equation 5x + 8 + x = 32 is x = 4.
1 answer