This study notes covers Worked Example 3: Compound Inequality within Linear Inequalities for GCSE Mathematics. Revise Linear Inequalities in Algebra for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 6 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Worked Example 3: Compound Inequality

Solve: -3 < 2x + 1 ≤ 7

Step 1 Subtract 1 from ALL three parts

-3 - 1 < 2x + 1 - 1 ≤ 7 - 1

-4 < 2x ≤ 6

Step 2 Divide ALL three parts by 2

-4 ÷ 2 < 2x ÷ 2 ≤ 6 ÷ 2

-2 < x ≤ 3

Step 3 List integer solutions

Integer solutions: -1, 0, 1, 2, 3

(Not -2 because x > -2, but includes 3 because x ≤ 3)

Practice questions for Linear Inequalities

Which of the following correctly describes how to represent x > 3 on a number line?

A. A closed (filled) circle at 3, with an arrow pointing to the right
B. An open (empty) circle at 3, with an arrow pointing to the right
C. An open (empty) circle at 3, with an arrow pointing to the left
D. A closed (filled) circle at 3, with an arrow pointing to the left

1 markfoundation

When solving an inequality, the direction of the inequality sign must reverse if you multiply or divide both sides by a negative number. Explain why this rule is necessary. You may use an example to support your explanation.

2 marksstandard

Quick recall flashcards

Open vs Closed Circle on a number line

Open circle (hollow) for < and > — endpoint NOT included. Closed circle (filled) for ≤ and ≥ — endpoint IS included.

The Flip Rule for inequalities

When you multiply or divide BOTH sides by a NEGATIVE number, you MUST reverse (flip) the inequality sign. Example: -2x > 6 becomes x < -3

Worked Example 3: Compound Inequality

Worked Example 3: Compound Inequality

Practice questions for Linear Inequalities

Quick recall flashcards

14 questions on Linear Inequalities — practise free