Edexcel GCSE Maths: Equations and Inequalities

The diagram shows a rectangle. The length of the rectangle is $(2x + 1)$(2x+1) cm and the width is $(x - 2)$(x−2) cm. (No diagram is needed; use the measurements given.)

The area of the rectangle is $20\ \text{cm}^2$20 cm2.

(a) Show that $2x^2 - 3x - 22 = 0$2x2−3x−22=0. (2 marks)

(b) Solve $2x^2 - 3x - 22 = 0$2x2−3x−22=0, giving your solutions correct to 2 decimal places. (3 marks)

Solve the simultaneous equations

$3x + 2y = 4,$3x+2y=4, $5x - 4y = 3.$5x−4y=3. (4 marks)

(a) Solve the inequality $4x - 7 \leq 2x + 5$4x−7≤2x+5. (2 marks)

(b) $n$n is an integer such that $-3 < n \leq 2$−3<n≤2. Write down all the possible values of $n$n. (2 marks)

By completing the square, solve $x^2 + 6x - 4 = 0$x2+6x−4=0. Give your solutions in the form $a \pm \sqrt{b}$a±b​, where $a$a and $b$b are integers. (3 marks)

Solve $\dfrac{5x - 1}{3} = x + 4$35x−1​=x+4. (2 marks)

Solve $7x + 4 = 25$7x+4=25. (1 mark)