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Worked Example 3: Compound Inequality

Part of Linear Inequalities — GCSE Mathematics

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 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 6 of 7

Practice

14 questions

Recall

11 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)

Keep building this topic

Read this section alongside the surrounding pages in Linear Inequalities. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 2: Negative Coefficient (FLIP!)Common Mistakes to AvoidNot Just Equals!The Four Inequality Symbols

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

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Worked Example 2: Negative Coefficient (FLIP!)

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Common Mistakes to Avoid