Writing and Graphing Inequalities: Grade 6 Math Worksheet Answer Key – PDF Download

Problem 1: Reading Inequality Symbols

1. \(x\) is greater than 7
2. \(y\) is less than or equal to 12
3. 3 is less than \(n\) (\(n\) is greater than 3)
4. \(p\) is greater than or equal to 0.5

Problem 2: Comparing Numbers

1. \(9 > 4\)
2. \(2.5 = 2.50\) and \(2.50 > 2.05\): \(2.5 > 2.05\)
3. \(\frac{3}{4} = 0.75\) and \(\frac{7}{10} = 0.70\): \(\frac{3}{4} > \frac{7}{10}\)
4. \(\frac{1}{3}\) is about \(0.333\), which is greater than \(0.3\): \(0.3 < \frac{1}{3}\)

Problem 3: Testing Values

1. \(8 > 6\) is true. Yes
2. \(10 < 10\) is false. No
3. \(4 \ge 4\) is true. Yes
4. \(3 \le 2.5\) is false. No

Problem 4: Writing Inequalities

1. \(x > 9\)
2. \(y < 15\)
3. \(n \ge 20\)
4. \(p \le 3.5\)

Problem 5: Graphing Inequalities

1. Open circle at \(3\), shaded to the right. See graph one.
2. Closed circle at \(5\), shaded to the left. See graph two.
3. Open circle at \(2\), shaded to the left. See graph three.

Problem 6: Reading Graphs

1. Open circle at \(4\), shaded right: \(x > 4\)
2. Closed circle at \(7\), shaded left: \(x \le 7\)

Problem 7: Infinitely Many Solutions

Check each number: \(3 > 2.5\), \(4 > 2.5\), and \(2.6 > 2.5\) are true, so 3, 4, and 2.6 are solutions. The number \(2.5\) is not a solution because \(2.5 > 2.5\) is false; neither is \(2\).

There are infinitely many solutions because after every solution, such as \(2.6\), \(2.51\), or \(2.501\), there is always another number that is still greater than \(2.5\).

Problem 8: Little League Ages

At most 12 includes 12, so the inequality is \(a \le 12\).

\(12 \le 12\) is true, so \(a = 12\) is a solution. \(13 \le 12\) is false, so \(a = 13\) is not.

Problem 9: Spending Limit

1. She can spend up to $20, so \(s \le 20\).
2. \(18.75 \le 20\) is true, so $18.75 is a solution. \(21 \le 20\) is false, so $21 is not.
3. Closed circle at \(20\), shaded to the left toward \(0\). See graph.

Problem 10: Roller Coaster

1. \(h \ge 48\)
2. \(45.5 \ge 48\) is false; \(48 \ge 48\) and \(51 \ge 48\) are true. Aisha and Noah can ride.
3. Closed circle at \(48\), shaded to the right. See graph.
4. \(45.5 + x = 48\), so \(x = 48 – 45.5 = \) \(2.5\) inches

See every chapter on the Grade 6 math page.