Solving Inequalities Practice Questions

Solve $7y - 3 < 4y + 9$

On the number line below, show the set of values of $n$ for which

$$-7 < 2n + 1 \le 5$$

Solve $5 - 2x \le 11$

Write your answer to part (a) using set notation.

Solve $3 < \dfrac{2x + 5}{3} \le 7$

Write down all the integers that satisfy $3 < \dfrac{2x + 5}{3} \le 7$

Solve $x^2 \ge 5x + 24$

Find the set of possible values of $x$.

Rashid is buying prizes for a school quiz.

He buys $n$ notebooks costing £$2.40$ each and one board game costing £$3.75$.

Rashid spends less than £$25$ in total.

Work out the greatest possible number of notebooks Rashid buys.

Solve

$$4 \le (x - 3)^2 < 25$$

Show all your working.