Solving 3(x - 2) + 4 = 2x + 7

Algebra 1 · Axiom Academy

EXAMPLE Solving 3(x - 2) + 4 = 2x + 7 Work a multi-step linear equation: distribute, combine like terms, isolate the variable, and check the answer. Solve the equation 3(x - 2) + 4 = 2x + 7 for x , watching out for the common mistakes along the way. Nice work — you solved a multi-step linear equation end to end. The reliable order: 1. Distribute: Expand terms in parentheses to clear them. 3(x-2) became 3x-6 — multiply the outside number by every term inside. 2. Combine like terms: Simplify each side first. The constants -6 and +4 combined to -2 , giving 3x - 2 = 2x + 7 . 3. Isolate the variable term: Subtract 2x from both sides to gather the x terms, leaving x - 2 = 7 . 4. Solve: Undo the -2 with the inverse operation (add 2 ) to get x = 9 . 5. Check: Substitute x = 9 back in — both sides equal 25 , confirming the answer. Distribute, combine, isolate, solve, check — the same five moves solve almost any linear equation.

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