1Cademy - Solving $$rac{2}{3}(3m - 6) = 5 - m$$ Using a General Strategy

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Linear Equation in One Variable

Example

Solving $rac{2}{3}(3m - 6) = 5 - m$ Using a General Strategy

To solve the linear equation $rac{2}{3}(3m - 6) = 5 - m$ , apply the general five-step strategy:

Step 1. Simplify both sides. Distribute the $rac{2}{3}$ into the parentheses on the left side. The product of $rac{2}{3}$ and $3m$ simplifies to $2m$ , and $rac{2}{3}$ times $-6$ simplifies to $-4$ : $2m - 4 = 5 - m$

Step 2. Collect all variable terms on one side. Add $m$ to both sides to bring the variables to the left side: $2m + m - 4 = 5 - m + m$ $3m - 4 = 5$

Step 3. Collect all constant terms on the other side. Add $4$ to both sides to bring the constants to the right side: $3m - 4 + 4 = 5 + 4$ $3m = 9$

Step 4. Make the coefficient of the variable term equal to 1. Divide both sides by $3$ : $rac{3m}{3} = rac{9}{3}$ $m = 3$

Step 5. Check the solution. Substitute $3$ for $m$ in the original equation: $rac{2}{3}(3(3) - 6) = 5 - 3$ $rac{2}{3}(9 - 6) = 2$ $rac{2}{3}(3) = 2$ $2 = 2$

Since the equation balances, the solution $m = 3$ is correct.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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