Equations with Brackets & Word Problems

≈ 25 min

When an equation contains brackets, expand first, then solve as usual:

2(x + 3) = 14

2x + 6 = 14 \qquad (\text{expand})

2x = 8 \qquad (\text{subtract } 6)

x = 4

The same idea turns a word problem into an equation. Read carefully, name the unknown, then solve. Many everyday shopping and travel problems become simple linear equations once you write them down.

Worked example. Solve $3(x - 1) = 2x + 4$ .

3x - 3 = 2x + 4 \qquad (\text{expand})

x - 3 = 4 \qquad (\text{subtract } 2x)

x = 7 \qquad (\text{add } 3)

Solve for $x$ : $2(x + 3) = 14$

Solving $5(x - 2) = 20$ , which is a correct first step?

Expand to get $5x - 10 = 20$

Write $5x - 2 = 20$

Subtract 5 from both sides

Add 2 to both sides to get $5x = 22$

Thabo buys 4 loaves of bread, each costing R $x$ . He pays with a R50 note and gets R6 change. Find the price of one loaf, in rand.

Solve and answer in the form x=…: $3(x - 1) = 2x + 4$