Equations with brackets and pronumerals on both sides

Expanding brackets to solve equations, and collecting pronumerals on one side when they appear on both sides.

Brackets

Example 1●

Solve $3(x - 4) = 15$.

$3x - 12 = 15$

Expand

$3x = 27$, so $x = 9$

Example 2●●

Solve $5x + 3 = 2x + 18$.

$3x + 3 = 18$

Subtract 2x

$3x = 15$, so $x = 5$

Example 3●●●

Solve $2(x + 5) = 4(x - 1)$.

$2x + 10 = 4x - 4$

$10 = 2x - 4$

Subtract 2x

$14 = 2x$, so $x = 7$

Flashcards

First step with brackets

Expand (or divide by the number outside).

$x$ on both sides

Subtract the smaller $x$ term from both sides.

$7x = 3x + 20$

$x = 5$

Practice