Linear Inequalities
Grade 4Inequalities and number lines
An inequality gives a range of values rather than one answer. The symbols are: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
You solve a linear inequality almost identically to a linear equation — with one critical difference.
The one rule that differs from equations
When you multiply or divide both sides of an inequality by a negative number, the inequality sign flips direction. So −2x < 6 becomes x > −3 after dividing by −2. Get this wrong and your answer points the wrong way.
Worked example
EXAMPLE
Solve 3x − 5 ≥ 7 and represent the answer on a number line.
Add 5 to both sides: 3x ≥ 12. Divide by 3 (positive, so sign stays): x ≥ 4. On a number line: closed circle at 4 (because ≥ includes 4), arrow pointing right. x ≥ 4.
Number line notation
On a number line, an open circle (○) means the endpoint is not included (use for < and >). A closed/filled circle (●) means the endpoint is included (use for ≤ and ≥).
Try this one
Solve the inequality
\[ 5x - 4 \geq 11 \]
[2]
Nova's hint:
Try to Solve it with Nova?
This is a linear inequality — solve it the same way you would a linear equation.
Ask yourself: 'what inverse operations do I need to isolate \(x\)?'
For example, for \( 4x - 3 \geq 9 \), add 3 to both sides to get \( 4x \geq 12 \), then divide by 4.
