Worksheets · Foundation and Higher

One-variable linear inequalities

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

Question 1Non-calculator · 3 marks
Answer each part.
(a) Solve $3x - 5 < 16$ (2)
(b) $n$ is an integer and $-2 < n \le 3$ . Write down all the possible values of $n$ . (1)
Question 2Non-calculator · 4 marks
$-4<2x+1\le 13$ , where x is an integer.
(a) Write all possible values of x. (2)
(b) Find the sum of all these values. (2)
Question 3Non-calculator · 6 marks
Answer each part.
(a) Solve $-7 \le 3x + 2 < 11$ (2)
(b) $x$ is an integer. It satisfies both $4x - 1 > 2x + 6$ and $\frac{x}{2} < 5$ . How many possible values of $x$ are there? (4)

Answers and marks

(a) $x < 7$

(b) $-1, 0, 1, 2, 3$

(a) -2, -1, 0, 1, 2, 3, 4, 5, 6

(b) $18$

(a) $-3 \le x < 3$

(b) $6$

One-variable linear inequalities

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