Worksheets · Foundation and Higher

Linear equations, including both sides

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 2 marks
(a) Solve 6x + 5 = 47. (2)
Question 2Non-calculator · 4 marks
A number x satisfies $3(4x-4)=2(4x+2)+4$ .
(a) Solve the equation. (3)
(b) Describe a check for your solution. (1)
Question 3Non-calculator · 6 marks
Show clear algebraic working.
(a) Solve $\dfrac{x + 4}{3} - \dfrac{x - 2}{4} = 2$ . You must show your working. (3)
(b) The mean of the four expressions $2x + 1$ , $3x - 2$ , $x + 7$ and $10$ is equal to $3x - 1$ . Find the value of $x$ . You must show your working. (3)

Answers and marks

(a) $7$

(a) $5$

(b) Substitute the value into both original bracketed sides and confirm that the two totals are equal.

C1 Correct conclusion with supporting reasoning: Substitute the value into both original bracketed sides and confirm that the two totals are equal.

(a) $x = 2$

M1 Multiplying through by 12 (or a common multiple) to clear both fractions, including the 2 on the right.
M1 Expanding to $4x + 16 - 3x + 6$ .
A1 The correct answer, $x = 2$ .

(b) $x = \dfrac{10}{3}$

Linear equations, including both sides

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