Linear Equations

One-Step Equations

Solve a linear equation that requires a single operation to isolate the variable.

one-step To solve x + c = d: subtract c from both sides to get x = d - c. The inverse operation undoes what was done to x.

Example

Subtract the same amount from both sides to isolate x.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x+7=12x+ 7 = 12
Keep both sides balanced.left sidex + 7right side12=both sidessubtract the same amount from both sides--=--check--Start: x + 7 = 12

Step 2 — Subtract from both sides

Subtract 7 from both sides.

x+7−7=12−7x+ 7 - \hl{7} = 12 - \hl{7}
Subtract 7 from both sides.left sidex + 7right side12=both sidessubtract 7: x + 7 - 7 = 12 - 7--=--check--Start: x + 7 = 12

Step 3 — Simplify

Simplify: 12 - 7 = 5.

x=12−7=5x = 12 - 7 = \hl{5}
Isolate x: 12 - 7 = 5.left sidex + 7right side12=both sidessubtract 7: x + 7 - 7 = 12 - 7x=5check--Start: x + 7 = 12

Step 4 — Check

Check: 5 + 7 = 12.

5+7=125 + 7 = \hl{12}
Check: 5 + 7 = 12.left sidex + 7right side12=both sidessubtract 7: x + 7 - 7 = 12 - 7x=5check5 + 7 = 12Start: x + 7 = 12

Step 5 — Result

Read the final result.

x=5x = 5
Result: x = 5.left sidex + 7right side12=both sidessubtract 7: x + 7 - 7 = 12 - 7x=5resultx = 5Start: x + 7 = 12