Equations with Brackets

≈ 25 min

Brackets mean multiplication of everything inside. Expand first, then solve as usual — the distributive law:

a(b + c) = ab + ac

Worked example. Solve $3(x - 2) = 12$ .

3x - 6 = 12 \qquad \text{(expand)}

3x = 18 \qquad \text{(add 6)}

x = 6

Shortcut worth knowing: when the bracket equals a number cleanly divisible, you may divide first: $3(x-2)=12 \Rightarrow x - 2 = 4 \Rightarrow x = 6$ . Both routes are legal; expansion always works.

Solve for $x$ : $3(x - 2) = 12$

Solve and answer in the form x=…: $2(x + 5) = 3(x - 1)$

Which is the correct expansion of $5(2x - 3)$ ?

$10x - 3$

$10x - 15$

$7x - 8$

$10x + 15$

Solve for $x$ : $4(2x - 1) = 28$