Linear Equations

Equations with Parentheses

Solve a linear equation containing parentheses by expanding with the distributive property, then solving the two-step result.

with-parentheses Expand a(x + b) = ab + ax first, then isolate the variable term and divide. Always distribute before solving.

Example

Distribute first, then solve the resulting equation.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

2(x+3)=142 (x+ 3 ) = 14
Start by distributing the outside 2.left side2(x + 3)=right side14arrowsoutside 2 points to both inside pieces--then subtract 6--divide by 2check--Start: 2(x + 3) = 14

Step 2 — Distribute

Distribute first: 2(x + 3) = 14.

2x+2×3=14\hlmath{2x} + \hl{2} \times \hl{3} = 14
Distribute 2 to x and 3.left side2(x + 3)=right side14arrows2 * x = 2x 2 * 3 = 6--then subtract 6--divide by 2check--Start: 2(x + 3) = 14

Step 3 — Simplify

Simplify the distribution: 2x + 6 = 14.

2x+6=142x + \hl{6} = 14
After distribution: 2x + 6 = 14.left side2(x + 3)=right side14arrows2 * x = 2x 2 * 3 = 62x + 6 = 14then subtract 6--divide by 2check--Start: 2(x + 3) = 14

Step 4 — Subtract constant

Subtract the constant: 14 - 6 = 8.

2x=14−6=82x = 14 - 6 = \hl{8}
Subtract 6 from both sides.left side2(x + 3)=right side14arrows2 * x = 2x 2 * 3 = 62x + 6 = 1414 - 6 = 82x = 8divide by 2check--Start: 2(x + 3) = 14

Step 5 — Divide

Divide to solve: 8 / 2 = 4.

x=8/2=4x = 8 / 2 = \hl{4}
Divide by 2: 8 / 2 = 4.left side2(x + 3)=right side14arrows2 * x = 2x 2 * 3 = 62x + 6 = 1414 - 6 = 82x = 88 / 2 = 4check--Start: 2(x + 3) = 14

Step 6 — Result

Read the final result.

x=4x = 4
Result: x = 4.left side2(x + 3)=right side14arrows2 * x = 2x 2 * 3 = 62x + 6 = 1414 - 6 = 82x = 88 / 2 = 4x = 42(4 + 3) = 14Start: 2(x + 3) = 14