These 10 problems practice reading, writing, testing, and graphing inequalities from Common Core 6.EE.B.5 and 6.EE.B.8. You compare numbers, test values for solutions, and graph with open and closed circles on number lines.
Problems 8 through 10 are word problems about ages, spending, and ride heights. Decide for each whether the boundary number is included.
Problem 1: Reading Inequality Symbols
Write each inequality in words.
- \(x > 7\)
- \(y \le 12\)
- \(3 < n\)
- \(p \ge 0.5\)
Problem 2: Comparing Numbers
Write the symbol < or > in each blank.
- \(9\) ___ \(4\)
- \(2.5\) ___ \(2.05\)
- \(\frac{3}{4}\) ___ \(\frac{7}{10}\)
- \(0.3\) ___ \(\frac{1}{3}\)
Problem 3: Testing Values
Decide whether the given value is a solution of the inequality. Show the substitution.
- \(x > 6\); \(x = 8\)
- \(x < 10\); \(x = 10\)
- \(x \ge 4\); \(x = 4\)
- \(x \le 2.5\); \(x = 3\)
Problem 4: Writing Inequalities
Write an inequality for each statement.
- \(x\) is greater than 9
- \(y\) is less than 15
- \(n\) is at least 20
- \(p\) is at most 3.5
Problem 5: Graphing Inequalities
Graph each inequality on its own number line from 0 to 10.
- \(x > 3\)
- \(x \le 5\)
- \(x < 2\)
Problem 6: Reading Graphs
Write the inequality shown by each graph.
Problem 7: Infinitely Many Solutions
List three different solutions of \(x > 2.5\) and one number that is not a solution. Explain why the inequality has infinitely many solutions.
Problem 8: Little League Ages
A Little League division is for players who are at most \(12\) years old. Write an inequality for a player’s age \(a\), then tell whether \(a = 12\) and \(a = 13\) are solutions.
Problem 9: Spending Limit
Maya has $20 to spend at the farmers market. Let \(s\) be the dollars she spends.
- Write an inequality for the amount she can spend.
- Is $18.75 a solution? Is $21?
- Graph the inequality on the number line below, using the numbers 0 to 24.
Problem 10: Roller Coaster
Riders on a roller coaster must be at least \(48\) inches tall. Jamal is \(45.5\) in. tall, Aisha is \(48\) in. tall, and Noah is \(51\) in. tall.
- Write an inequality for a rider’s height \(h\).
- Which of the three riders can ride?
- Graph the inequality on the number line below.
- Write and solve an equation to find how many more inches Jamal must grow to reach the minimum height.
See every chapter on the Grade 6 math page.