Question

Distributing a Negative Sign
Generate a plan and describe the steps needed to solve the equation.

34 = –(m + 3)

Answer 1

Plan
1. Remove the parentheses by distributing the negative sign across the terms inside.
2. Use inverse operations to isolate m (undo addition/subtraction, then multiplication/division).
3. Solve for m and check the solution by substituting back.

Steps
1. Start with: 34 = −(m + 3)
2. Distribute the negative sign: 34 = −m − 3 (because −(m) = −m and −(3) = −3)
3. Add 3 to both sides to isolate the term with m: 34 + 3 = −m → 37 = −m
4. Multiply both sides by −1 (or divide both sides by −1) to get m by itself: m = −37
5. Check: substitute m = −37 into the original equation: −(−37 + 3) = −(−34) = 34, which matches the left side.

Solution: m = −37.