Inequalities

Algebra

Questions marked Higher are aimed at the Higher tier.

These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.

Solve $x + 5 > 12$.

2 marks
Solve $3x \le 18$.

2 marks
Solve $2x - 1 < 9$.

3 marks
Solve $5 - x \ge 2$.

3 marks
Solve $-2 < x + 1 \le 4$.

4 marks
Solve $3 < 2x + 1 < 11$.

4 marks
Solve $x^{2} - 5x + 6 < 0$. Higher

5 marks
Solve $4x + 3 > 2x - 5$ and $x^{2} - x - 6 \ge 0$. List the integers from $-5$ to $6$ inclusive that satisfy both. Higher

6 marks

Mark scheme

Answer. $x > 7$
- Subtract $5$.
- $x > 7$
Answer. $x \le 6$
- Divide by $3$.
- $x \le 6$
Answer. $x < 5$
- $2x < 10$
- $x < 5$
Answer. $x \le 3$
- $-x \ge -3$
- Dividing by $-1$ reverses the sign: $x \le 3$.
Answer. $-3 < x \le 3$
- Subtract $1$ throughout.
- $-3 < x \le 3$
Answer. $1 < x < 5$
- $2 < 2x < 10$
- $1 < x < 5$
Answer. $2 < x < 3$
- $(x - 2)(x - 3) < 0$
- The product is negative between the roots.
- $2 < x < 3$
Answer. $x > -4$, and $x \le -2$ or $x \ge 3$. The integers are $-3, -2, 3, 4, 5, 6$.
- $2x > -8$, so $x > -4$.
- $(x - 3)(x + 2) \ge 0$, so $x \le -2$ or $x \ge 3$.
- The integers in the closed range that satisfy both are $-3, -2, 3, 4, 5, 6$.