Foundation and Higher · forming equations
Turn the words
into an equation.
Then solve it.
let x be the thing
you do not know
they all start the same way —
Let x be…
name the unknown
write everything else using x
type 1 of 4
Think of a number
1. Call it n. Follow the words in order.
2. Solve it like any equation.
✓ Check: 5 × 3 + 4 = 19
“I think of a number, multiply it by 3, add 4 and get 19.”
3n + 4 = 19
3n = 15 − 4
n = 5 ÷ 3
type 2 of 4
Perimeter
1. Perimeter: add all four sides.
2. Collect like terms, then solve: 4x = 20.
✓ The sides are 5 cm and 8 cm
A rectangle has sides x and x + 3. Its perimeter is 26 cm.
x + x + 3 + x + x + 3 = 26
4x + 6 = 26 collect
x = 5
type 3 of 4
Angles
1. Angles in a triangle add to 180°.
2. Collect, then divide: x = 30.
✓ The angles are 30°, 60° and 90°
The angles in a triangle are x, 2x and 3x.
x + 2x + 3x = 180
6x = 180
x = 30
type 4 of 4
Answer the question
1. Tom is x, so Sam is x + 4.
2. x = 13 is Tom’s age, not the answer.
✓ Re-read it: how old is Sam?
Sam is 4 years older than Tom. Their ages add up to 30. How old is Sam?
x + x + 4 = 30 Tom is x
2x = 26, so x = 13
Sam is 13 + 4 = 17
forming and solving —
Name it
let x be the unknown
Build it
use the fact in the question
Solve it
then answer what was asked
x is rarely the final answer.
Go back and read the question.
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