Questions: What value of m makes the equation 2m+12=7m-3 true? Enter the answer in the box provided. m=

Solution Steps

To solve the equation \( |2m + 12| = 7m - 3 \), we need to consider the definition of absolute value, which leads to two separate cases: one where the expression inside the absolute value is non-negative and one where it is negative. We then solve each resulting equation for \( m \) and check which solutions satisfy the original equation.

Given the equation \( |2m + 12| = 7m - 3 \), we need to consider two cases:

1. \( 2m + 12 = 7m - 3 \)
2. \( -(2m + 12) = 7m - 3 \)

\[ 2m + 12 = 7m - 3 \] \[ 12 + 3 = 7m - 2m \] \[ 15 = 5m \] \[ m = 3 \]

\[ -2m - 12 = 7m - 3 \] \[ -12 + 3 = 7m + 2m \] \[ -9 = 9m \] \[ m = -1 \]

We need to check which solutions satisfy the original equation \( |2m + 12| = 7m - 3 \).

\[ |2(3) + 12| = 7(3) - 3 \] \[ |6 + 12| = 21 - 3 \] \[ |18| = 18 \] This is true.

\[ |2(-1) + 12| = 7(-1) - 3 \] \[ |-2 + 12| = -7 - 3 \] \[ |10| = -10 \] This is false.

Final Answer