Solve an Equation with the Distributive Property

Problem

3(x + 4) = 27

Answer

x = 5

The distributive property says that a factor in front of parentheses multiplies every term inside. Clear the parentheses first, then the equation is a normal two-step problem.

Step-by-step solution

Distribute the 3 to both terms inside the parentheses.
$3(x + 4) = 3x + 12$
Why: The 3 multiplies the whole group, not just the first term.
Rewrite the equation.
$3x + 12 = 27$
Why: The left side is now a plain two-step expression.
Subtract 12 from both sides.
$3x = 15$
Why: Subtracting undoes the addition.
Divide both sides by 3.
$x = 5$
Why: Dividing undoes the multiplication.

Common mistakes

Multiplying only 3 x x and leaving the 4 alone.
Subtracting before distributing.
Dividing 15 by 5 instead of by 3.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$2(x + 3) = 14$

Show answer

$x = 4$
$5(x - 2) = 20$

Show answer

$x = 6$
$4(x + 1) = 24$

Show answer

$x = 5$
$3(2x - 1) = 15$

Show answer

$x = 3$
$2(3x + 4) = 26$

Show answer

$x = 3$