Solving One and Two-Step Equations

One-Step Equations

Use inverse operations to isolate the variable:

$x + 7 = 12 \implies x = 12 - 7 = 5$ $x - 3 = 9 \implies x = 9 + 3 = 12$ $4x = 28 \implies x = 28 \div 4 = 7$ $\frac{x}{5} = 6 \implies x = 6 \times 5 = 30$

Two-Step Equations

Undo addition/subtraction first, then multiplication/division:

$2x + 5 = 13$ $2x = 8$ $x = 4$

$\frac{x}{3} - 4 = 2$ $\frac{x}{3} = 6$ $x = 18$

Equations with Negative Numbers

$-3x + 9 = 0$ $-3x = -9$ $x = 3$

Checking Your Solution

Always substitute back: If $x = 4$ in $2x + 5 = 13$: $2(4) + 5 = 8 + 5 = 13$ ✓

Writing Equations from Words

| Words | Equation | |-------|---------| | "5 more than a number is 12" | $n + 5 = 12$ | | "A number divided by 3 equals 7" | $\frac{n}{3} = 7$ | | "Twice a number minus 4 is 10" | $2n - 4 = 10$ |

Golden rule: Whatever you do to one side, do to the other. Keep the equation balanced!