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Solving Multi-Step Linear Equations

5 min readGrade 9 · Algebra & Patterning

Multi-step equations bring every algebra skill together: distribute, collect like terms, gather variables on one side, and isolate the unknown — then check by substitution.

What students explore

Students solve linear equations that require distribution, collecting like terms, and variables on both sides, including rational coefficients and solutions.

Key ideas

Preserve equality: any operation done to one side must be done to the other. A reliable order is distribute, collect like terms, move variables to one side, then isolate. Always verify by substituting the solution back in.

Worked example

Solve 3(x − 4) = 2x + 5: distribute to get 3x − 12 = 2x + 5; subtract 2x to get x − 12 = 5; add 12 to get x = 17. Check: 3(17 − 4) = 39 and 2(17) + 5 = 39. ✓

KEY VOCABULARY

Distributive property — a(b + c) = ab + ac; multiply the outside term by each term inside.

Like terms — Terms with the same variable that can be combined.

Inverse operation — An operation that undoes another, used to isolate the variable.

Solution — The value of the variable that makes the equation true.