Linear Equations

Two-Step Equations

Solve a linear equation that requires two operations to isolate the variable: first remove the constant, then divide.

two-step To solve ax - b = d: add b to both sides, then divide by a. Undo operations in reverse order of operations.

Example

Undo the constant, then divide both sides.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

3x−4=113x - 4 = 11
Start with both sides balanced.left side3x - 4=right side11both sidesfirst undo the -4--then undo 3 times x--checkresultStart: 3x - 4 = 11

Step 2 — Add to both sides

Add 4 to both sides.

3x−4+4=11+43x - 4 + \hl{4} = 11 + \hl{4}
Add 4 to both sides.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 4--then undo 3 times x--checkresultStart: 3x - 4 = 11

Step 3 — Simplify

After adding, the equation is 3x = 15.

3x=153x = \hl{15}
After adding: 3x = 15.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 43x = 15then undo 3 times x--checkresultStart: 3x - 4 = 11

Step 4 — Divide both sides

Divide both sides by 3: 3/3 and 15/3.

33x=153\hlmath{\frac{3}{3}} x = \hlmath{\frac{15}{3}}
Divide both sides by 3.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 43x = 15divide by 3: 15 / 3 = 5--checkresultStart: 3x - 4 = 11

Step 5 — Simplify

Simplify to solve: x = 5.

x=5x = \hl{5}
Isolate x: x = 5.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 43x = 15divide by 3: 15 / 3 = 5x = 5checkresultStart: 3x - 4 = 11

Step 6 — Check

Check: 3 x 5 - 4 = 11.

3x×5−4=113x \times 5 - 4 = \hl{11}
Check: 3 x 5 - 4 = 11.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 43x = 15divide by 3: 15 / 3 = 5x = 53 x 5 - 4 = 11resultStart: 3x - 4 = 11

Step 7 — Result

Read the final result.

x=5x = 5
Result: x = 5.left side3x - 4=right side11both sidesadd 4: 3x - 4 + 4 = 11 + 43x = 15divide by 3: 15 / 3 = 5x = 5checkx = 5Start: 3x - 4 = 11