Medium📚 Inequalities

Solving Inequalities Example

Grades 7-8Key Stage 3-4Årskurs 8-9

Problem

Solve and graph: -3x + 7 > 16

📝Step-by-Step Solution

Isolate the variable term

Subtract 7 from both sides: -3x + 7 - 7 > 16 - 7

-3x > 9

Divide by the coefficient

Divide both sides by -3. IMPORTANT: When dividing by a negative number, FLIP the inequality sign!

-3x ÷ (-3) < 9 ÷ (-3)

Write the solution

x < -3

Graph on a number line

Draw an open circle at -3 (because x is NOT equal to -3), then shade to the LEFT (because x is less than -3).

Check with a test value

Try x = -4: -3(-4) + 7 = 12 + 7 = 19 > 16 ✓. Try x = 0: -3(0) + 7 = 7 > 16 ✗. Correct!

✅Final Answer

x < -3

CRITICAL RULE: When multiplying or dividing both sides of an inequality by a negative number, you MUST flip the inequality sign (< becomes >, ≤ becomes ≥, etc.). This is the most common mistake in solving inequalities!

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