Solve for m.

Question

–
3≤
m–2
2
<4
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequality \(-3 \leq \frac{m - 2}{2} < 4\), we can break it down into two parts.

1. Starting with the left part of the compound inequality: \[ -3 \leq \frac{m - 2}{2} \] Multiply both sides by 2 (since 2 is positive, the direction of the inequality will not change): \[ -6 \leq m - 2 \] Now add 2 to both sides: \[ -4 \leq m \]

2. Now for the right part of the compound inequality: \[ \frac{m - 2}{2} < 4 \] Again, multiply both sides by 2: \[ m - 2 < 8 \] Add 2 to both sides: \[ m < 10 \]

Putting both parts together, we get the compound inequality: \[ -4 \leq m < 10 \]

Thus, the final answer is: \[ -4 \leq m < 10 \]