What value of m makes the equation 2(3m +2) =2(m - 4) + 24 true?
A.) 3
B.) 4
C.) 5
D.) 9
Let's solve the equation step by step:
2(3m + 2) = 2(m - 4) + 24
First, distribute the 2 on the left side:
6m + 4 = 2(m - 4) + 24
Next, distribute the 2 on the right side:
6m + 4 = 2m - 8 + 24
Combine like terms on the right side:
6m + 4 = 2m + 16
Next, subtract 2m from both sides:
6m - 2m + 4 = 2m - 2m + 16
4m + 4 = 16
Next, subtract 4 from both sides:
4m + 4 - 4 = 16 - 4
4m = 12
Finally, divide both sides by 4 to solve for m:
m = 12/4
Simplifying:
m = 3
Therefore, the value of m that makes the equation true is 3.
The correct answer is A.) 3.