Solving Linear Equations

An equation says two expressions are equal. Whatever you do to one side, do to the other — add, subtract, multiply, or divide by the same non-zero number — and the balance stays true.

The balance idea

An equation says two expressions are equal. Whatever you do to one side, do to the other — add, subtract, multiply, or divide by the same non-zero number — and the balance stays true.

A reliable solve checklist

Expand parentheses with the distributive property.
Combine like terms on each side.
Move variable terms to one side and constants to the other.
Divide by the coefficient of the variable.
Check by substituting back into the original equation.

Worked example

Solve 3(x − 2) + 4 = 2x + 9.

Expand: 3x − 6 + 4 = 2x + 9 → 3x − 2 = 2x + 9. Subtract 2x: x − 2 = 9. Add 2: x = 11. Check: 3(9)+4 = 31 and 2(11)+9 = 31. ✓

If you end with a true statement like 0 = 0, every real number works (identity). If you end with 0 = 5, there is no solution.