AQA GCSE · Mathematics 8300

Solving equations and inequalities: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Solving equations and inequalities.

10 questions21 marksFree, no account

Question 1

1 mark

Solve the following linear equation for \(y\):
\(5y - 7 = 18\)

Question 2

1 mark

Solve the following simultaneous equations to find the value of \(x\) and \(y\):
\(5x + 3y = 21\)
\(4x - 3y = 6\)

Question 3

1 mark

Find the set of integer values for \(x\) that satisfy the double inequality:
\(2 < 3x - 1 \le 14\)

Question 4

1 mark

Find the largest integer value of \(n\) that satisfies the inequality:
\(2n + 5 < 16\)

Question 5

1 mark

Solve the linear equation for \(a\):
\(7a - 3 = 3a + 17\)

Question 6

2 marks

Solve the inequality:
\( 4x - 7 > 13 \)
Represent your answer using inequality notation.

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Solve the inequality \(3(x + 4) < 21\) and represent your answer using inequality notation.

Write your answer out first, then check it against the worked solution.

Question 8

2 marks

Solve the following equation for \(x\):
\(5x - 12 = 18\)

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

Part a: Solve the inequality:
\(7n - 5 < 16\)

Part b: Write down the largest integer value of \(n\) that satisfies the inequality from part (a).

Part c: Solve the equation for \(z\):
\(\frac{z}{3} + 4 = 10\)

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

A rectangle has a length of \(2x + 3\) cm and a width of \(x - 1\) cm.

(a) The perimeter of the rectangle is 28 cm. Form an equation in terms of \(x\) and solve it to find the value of \(x\).
(b) Using your value of \(x\) from part (a), calculate the area of the rectangle.
(c) Solve the inequality \(5y - 4 < 3y + 10\) and show the solution on a number line.

Write your answer out first, then check it against the worked solution.

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