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Graphing Inequalities on Number Lines
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Graphing Inequalities on Number Lines
Help organise a community festival by solving and graphing inequalities. For each number line, use an open circle when the endpoint is not included and a closed circle when it is included. Shade or draw an arrow towards all values that satisfy the inequality. Show working where needed.
Read and interpret
1.A festival ride is suitable for visitors taller than 140 cm. Which inequality describes the height h, and is 140 cm included?
- h > 140; 140 cm is not included
- h ≥ 140; 140 cm is included
- h < 140; 140 cm is not included
- h ≤ 140; 140 cm is included
2.The festival entry fee is at most $18. Let c be the fee in dollars. Write an inequality for c and state whether $18 is allowed.
3.Graph the ride-height condition h > 140. Mark the endpoint and show all allowed heights on the number line.
Solve, then graph
4.A food stall needs to sell more than 36 drinks to cover its costs. If it has already sold 11 drinks, write and solve an inequality for the additional number n it must sell.
5.Solve 3x − 5 ≤ 16, then graph the solution set.
6.A festival game requires a score of at least 50 points. A player has 8 points already and earns 7 points per round. Write and solve an inequality for the number r of rounds needed.
7.Solve −2x + 3 > 11, then graph the solution. Remember to reverse the inequality when dividing by a negative number.
Compound conditions and reasoning
8.Festival volunteer shifts must last at least 3 hours but less than 7 hours. Let t be the shift length in hours. Write the compound inequality and graph it.
9.Solve the compound inequality −4 ≤ 2x + 2 < 10, then state the solution using inequality notation.
10.A ticket price p must be no more than $25 and greater than $12. Choose the correct interval description.
- 12 < p ≤ 25
- 12 ≤ p < 25
- p < 12 or p > 25
- 12 ≤ p ≤ 25
11.Kai graphs x ≥ 2 with an open circle at 2 and an arrow pointing right. Identify the error and describe the correct graph.
3 printable pages
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