KS3 Maths · Year 7 · Chapter 15: Equations and formulae · Lesson 2

Equations with the variable on both sides

Year 7About 60 minutesNo calculator53 marks

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Date

Do Now

Quick questions to start.

A1
Needed today
Solve $5 x - 8 = 27$ .
[1 mark]
Answer
A2
Needed today
Simplify $9 x + 4 - 6 x - 10$ .
[1 mark]
Answer
A3
Last lesson
Solve $4 (x - 6) = 10$ .
[1 mark]
Answer
A4
From chapter 14
A circle has diameter $8$ cm. Work out its circumference. Give your answer in terms of $π$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Solve $5 x + 9 = 2 x + 30$ . Check your answer.

Hint Subtract

2 x

from both sides, so that

x

is on one side only.

B1
Solve $7 x - 11 = 3 x + 13$ .
[2 marks]
Answer

Example 2

Solve $3 x - 5 = 31 - x$ .

Hint The right-hand side has

- x

. Add

x

to both sides.

B2
Solve $2 x + 9 = 44 - 3 x$ .
[2 marks]
Answer

Example 3

Solve $3 (x + 6) = 9 x - 12$ . Use two different methods.

Hint Method 1: expand the bracket. Method 2:

3

divides

9 x

and

12

, so divide both sides by

3

first.

B3
Solve $4 (x - 2) = 6 x - 19$ .
[3 marks]
Answer

Example 4

Solve $5 (x - 3) = 2 (x + 6)$ .

Hint Expand both brackets first.

B4
Solve $3 (2 x + 1) = 4 (x + 5)$ .
[3 marks]
Answer

Example 5

Mia thinks of a number. She multiplies it by $5$ and subtracts $8$ . She gets the same answer when she multiplies the number by $3$ and adds $11$ . Write an equation and solve it to find Mia's number.

Hint Call the number

n

. Write each instruction as an expression in

n

, and set the two expressions equal.

B5
Tom thinks of a number. He adds $4$ and then multiplies by $3$ . He gets the same answer when he doubles the number and adds $27$ . Write an equation and solve it to find Tom's number.
[3 marks]
Answer

Practice

Year 7

C1
Solve $9 + 2 x = 4 x - 15$ .
[2 marks]
Answer
C2
Solve $3 x + 20 = 5 - 2 x$ .
[2 marks]
Answer

C3
Solve $6 x - 4 = 2 x + 7$ . Give your answer as a mixed number.
[2 marks]
Answer
C4
Solve $18 - 3 x = 2 - x$ .
[2 marks]
Answer
C5
Solve $2 (x - 7) = 5 x + 4$ .
[3 marks]
Answer
C6
Is $x = 4$ the solution of $7 x - 9 = 3 x + 5$ ? Show how you decide.
[2 marks]
AnswerYes / No

Exam-style questions

GCSE Foundation

D1
Priya solves $6 x + 5 = 2 x + 21$ . She writes: $6 x - 2 x = 21 + 5$ , so $4 x = 26$ and $x = 6.5$ .
Priya's answer is wrong. Explain the mistake she made, and solve the equation correctly.
[3 marks]
Answer

D2
Line $A$ and line $B$ are the same length. Line $B$ is made of two parts.
Not drawn accurately
(a)
Write down an equation in $x$ .
[1 mark]
Answer
(b)
Work out the length of line $A$ .
[3 marks]
Answer
Total for D2: 4 marks
D3
The rectangle and the square have the same perimeter.
Not drawn accurately
(a)
Show that $6 x + 4 = 4 x + 16$ .
[2 marks]
(b)
Work out the value of $x$ .
[1 mark]
Answer
(c)
Which shape has the larger area? You must show your working.
[2 marks]
Answer $\dots\dots\dots\dots$
Total for D3: 5 marks
D4
$A B C$ is an isosceles triangle with $A B = A C$ . Work out the perimeter of the triangle.
[4 marks]
Not drawn accurately
Answer
D5
A gym has two plans. Plan A costs £ $20$ to join and then £ $6$ for each visit. Plan B costs £ $44$ to join and then £ $3$ for each visit. For how many visits do the two plans cost the same? You must show your working.
[3 marks]
Answer

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Amir is three times as old as his sister Bella. In $12$ years' time, Amir will be twice as old as Bella. How old are Amir and Bella now?
[4 marks]
Hint 1 · What to try
Call Bella's age now $b$ . Write Amir's age now, and both ages in $12$ years, in terms of $b$ .
Hint 2 · The first line
In $12$ years Amir is $3 b + 12$ and Bella is $b + 12$ , so $3 b + 12 = 2 (b + 12)$ .
Hint 3 · The full method
$3 b + 12 = 2 b + 24$ , so $b = 12$ . Bella is $12$ and Amir is $36$ . Check: in $12$ years they are $48$ and $24$ .
AnswerAmir $\dots\dots$ Bella $\dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can solve an equation with the unknown on both sides.
I can solve such equations when they have brackets.
I can check a solution by substituting it into both sides.
I can write an equation from a problem and solve it.

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