MathsFreePrintable
Justifying Inequality Solutions
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Name:Date:
Justifying Inequality Solutions
Show the steps in your working. When asked to justify a solution, explain how you checked it.
Inequality essentials
1.Which symbol means “less than or equal to”?
- <
- ≤
- >
- ≥
2.For the inequality x > −2, which graph description is correct?
- An open circle at −2, with the line shaded to the right
- A closed circle at −2, with the line shaded to the right
- An open circle at −2, with the line shaded to the left
- A closed circle at −2, with the line shaded to the left
3.Which methods can provide evidence that a value satisfies an inequality? Select all that apply.
- Substitute the value into the original inequality; check a test value from the proposed solution region; compare the solution with a graph of the inequality
- Choose a value at random and assume it works
Solve and justify
4.Solve 4x − 7 ≤ 13. Then check the boundary value by substituting it into the original inequality and state whether it satisfies the inequality.
5.At a bush regeneration day, Talia has $36 to spend on native seedlings costing $8 each. Let n be the number of seedlings. Write an inequality for her spending, solve it, and explain why the number of seedlings must be a whole number.
6.Check whether x = −1 is a solution of 3x + 4 > 0. Substitute the value and use the resulting comparison to justify your answer.
7.Solve −2x + 6 ≥ 10. Show why the inequality symbol changes direction when you isolate x, then represent the solution on the number line.
8.A volunteer says that 5 is a solution of 2x − 3 < 8. Use substitution to decide whether the volunteer is correct, and justify your decision.
9.A creek-side thermometer must stay at or below 28°C during a monitoring session. The temperature is currently 21°C and rises by 2°C each hour. If h is the number of hours, write and solve an inequality for how long the temperature can rise before reaching the limit. Explain what the solution means.
2 printable pages
Page 1
Page 2
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
