9) Drag and drop the correct steps to solve the equation for x. Make sure to put the steps in order. Not all steps listed will be used. 12−3x=8−4(2x−6)
options: 12-3x=8-8x+24, 12-3x=32-8x, 12+5x=32, 12-3x=8-8x-24, 5x=20, 12-5x=-16, 12-3x=-16-18x, x=28, x=4
1) Distribute the -4 to the terms inside the parentheses: 12 - 3x = 8 - 8x + 24
2) Combine like terms: 12 - 3x = 32 - 8x
3) Add 8x to both sides: 12 + 5x = 32
4) Subtract 12 from both sides: 5x = 20
5) Divide both sides by 5: x = 4
10) Which equation has no solution? Select all that apply. (1 point) Responses 36−7y=−7(y−5)
8k+38=−3(−6−4k)
−4(x+3)=−12−4x
−2(w−2)=−3−2w
To determine which equation has no solution, we need to solve each equation and see if there is a value of the variable that satisfies the equation.
1) 36 - 7y = -7(y - 5)
Expanding the right side: 36 - 7y = -7y + 35
Combining like terms: 36 = 35
This equation does not hold true, so there is no solution.
2) 8k + 38 = -3(-6 - 4k)
Expanding the right side: 8k + 38 = 18 + 12k
Combining like terms: 8k + 38 = 12k + 18
Subtracting 12k from both sides: -4k + 38 = 18
Subtracting 38 from both sides: -4k = -20
Dividing by -4: k = 5
This equation has a solution (k = 5).
3) -4(x + 3) = -12 - 4x
Distributing: -4x - 12 = -12 - 4x
Combining like terms: -4x = -4x
This equation holds true for any value of x, so it has infinitely many solutions.
4) -2(w - 2) = -3 - 2w
Distributing: -2w + 4 = -3 - 2w
Combining like terms: -2w = -2w - 7
Subtracting -2w from both sides: 0 = -7
This equation does not hold true, so there is no solution.
Therefore, the equations that have no solution are:
1) 36 - 7y = -7(y - 5)
4) -2(w - 2) = -3 - 2w
Is the equation true, false, or open? 7m+10=3m+26
To determine if the equation 7m + 10 = 3m + 26 is true, false, or open, we need to simplify it further and see if a solution can be found.
Combining like terms on both sides of the equation, we get:
7m + 10 = 3m + 26
Subtracting 3m from both sides:
4m + 10 = 26
Subtracting 10 from both sides:
4m = 16
Dividing both sides by 4:
m = 4
Since a solution (m = 4) has been found, the equation is true.
Drag and drop the correct steps to solve the equation for x. Make sure to put the steps in order. Not all steps listed will be used.
2(x - 4) - 2x = 2x - 10
8 = 2x - 10
- 8 = 2x - 10
2 = 2x
2x + 8 - 2x = 2x - 10
2x - 8 - 2x = 2x - 10
18 = 2x
x = 9
x = 1
1) Distribute the 2 to the terms inside the parentheses: 2x - 8 - 2x = 2x - 10
2) Combine like terms: -8 = -10
3) No solution is found.
4) Combine like terms: 2x + 8 - 2x = 2x - 10
5) Combine like terms: -8 = -10
6) No solution is found.
7) Combine like terms: 18 = 2x
8) Divide both sides by 2: x = 9
9) Combine like terms: 2 = 2x
10) Divide both sides by 2: x = 1
The correct steps in order are:
1) Distribute the 2 to the terms inside the parentheses: 2x - 8 - 2x = 2x - 10
4) Combine like terms: 2x + 8 - 2x = 2x - 10
8) Divide both sides by 2: x = 9
9) Combine like terms: 2 = 2x
10) Divide both sides by 2: x = 1
are you sure
Apologies for the confusion earlier. Let's go through the steps again for solving the equation 2(x - 4) - 2x = 2x - 10:
1) Distribute the 2 to the terms inside the parentheses: 2x - 8 - 2x = 2x - 10
2) Combine like terms: -8 = -10
The equation -8 = -10 is not true. Therefore, there is no solution to the equation.
To solve the equation 12 - 3x = 8 - 4(2x - 6), we can follow these steps:
Step 1: Simplify both sides of the equation by distributing the -4 into the expression within the parentheses.
The equation becomes: 12 - 3x = 8 - 8x + 24
Step 2: Combine like terms on both sides of the equation.
The equation becomes: 12 - 3x = 32 - 8x
Step 3: Move the variable terms (in this case, -3x and -8x) to one side of the equation.
By adding 8x to both sides, we get: 12 + 5x = 32
Step 4: Move the constant terms (in this case, 12 and 32) to the opposite side of the equation.
By subtracting 12 from both sides, we get: 5x = 20
Step 5: Solve for x by isolating the variable.
Dividing both sides by 5, we get: x = 4
So the correct order of steps to solve the equation for x is:
12 - 3x = 8 - 4(2x - 6)
12 - 3x = 8 - 8x + 24
12 - 3x = 32 - 8x
12 + 5x = 32
5x = 20
x = 4
Option: x = 4 is the correct answer.