Inequalities (One Variable) • Topic 1 of 1

Solving & Graphing Inequalities

Inequalities compare expressions using symbols instead of an equals sign.

Symbol	Meaning	Graph (circle type)
<	less than	open circle (not included)
>	greater than	open circle (not included)
≤	less than or equal to	closed circle (included)
≥	greater than or equal to	closed circle (included)

Critical Rule: When you multiply or divide both sides by a negative number, you must reverse (flip) the inequality sign!

Example: -2x < 10 => divide by -2, flip sign => x > -5

NUMBER LINE GRAPHS:

x > 3:   <----|----o====>
              0    3
  (open circle at 3, shade right)

x <= -2: <====o----|----|-->
             -2    0    3
  (closed circle at -2, shade left)

-4 <= x < 2:
         <====o----o====>
             -4         2
  (closed at -4, open at 2)

CRITICAL RULE: Multiply/divide by NEGATIVE -> FLIP sign!

Solved Examples

Worked Example

Solve: x + 5 > 12 and graph.

Solutionx > 7. Open circle at 7, shade to the right.

Worked Example

Solve: 3y <= 21

Solutiony <= 7. Closed circle at 7, shade to the left.

Worked Example

Solve: -2z < 10

SolutionDivide by -2 and FLIP sign: z > -5. Open circle at -5, shade right.

Key Points

Open circle = < or > (value not included)
Closed circle = <= or >= (value is included)
Reverse the inequality sign when multiplying or dividing by a negative number
At least = >=, at most = <=, more than = >, fewer than = <

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The symbol $\ge$ means:

Explanation: $\ge$.

Q2.Multiplying or dividing an inequality by a negative number:

Explanation: Flip the sign.

Q3.The solution $x>2$ on a number line uses an:

Explanation: Open circle (strict).

Q4.Solve $x+3>7$:

Explanation: $x>4$.

Practice more MCQs → 📝 Assignment · 35 marks