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Algebraic Inequalities Exploration
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Algebraic Inequalities Exploration
Choose the best answer where options are given. For written questions, show your working and use the number lines to represent your solutions.
Symbols and meaning
Read each inequality carefully. Pay attention to whether the boundary value is included.
1.A swimming pool is open to children aged 12 and over. If a child's age is a years, which inequality describes the age rule?
- a > 12
- a ≥ 12
- a < 12
- a ≤ 12
2.Max has fewer than 9 trading cards. If c is the number of cards, which inequality represents this?
- c > 9
- c ≥ 9
- c < 9
- c = 9
3.Solve the inequality x + 5 < 11. Which answer is correct?
- x < 6
- x > 6
- x ≤ 6
- x = 6
4.Select every inequality that means a value is at most 8.
- x ≤ 8
- x < 8
- x = 8
- x ≥ 8
Write, solve and represent
Use inverse operations to solve. For each number-line diagram, mark the endpoint and show which values are solutions.
5.A local sports club requires members to be older than 14 years. Let a represent a member's age. Write an inequality for the rule.
6.Solve 3x − 2 ≥ 10. Show your working and represent the solution on the number line.
7.Solve 4x < 2x + 10. Show your working and represent the solution on the number line.
8.A bike hire costs $6 to unlock and $4 for each hour. Jai has no more than $26 to spend. Let h be the number of hire hours. Write an inequality for this situation, solve it, and describe how its solution would look on a number line.
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