Linear Inequalities: math practice, Grade 9 – download the PDF

1 Words to symbols ★★★

Write an inequality for each statement, using \(x\) for the number.

1. \(x\) is at least 18.
2. \(x\) is fewer than 12.
3. \(x\) is no more than 40.
4. \(x\) is more than 7.
5. \(x\) is at most 9.
6. \(x\) is a minimum of 5.

2 Testing solutions ★★★

Which of the numbers 5, 4, 6, and \(-2\) are solutions of \(3x-4<11\)?

3 One-step inequalities ★★★

Solve each inequality.

1. \(x+7\le 12\)
2. \(x-4>-1\)
3. \(6x<54\)
4. \(\dfrac{x}{5}\ge 3\)

4 Flip the sign ★★★

Solve each inequality.

1. \(-3x<18\)
2. \(-x\ge 5\)
3. \(\dfrac{x}{-4}>2\)
4. \(-7x\le -21\)

5 Reading a graph ★★★

Write the inequality shown by each number line.

The first graph is on top, the second below it.

6 Drawing graphs ★★★

Draw a number line and graph each solution set: (a) \(x>1\), (b) \(x\le -3\).

7 Two-step inequalities ★★★

Solve each inequality.

1. \(2x+3>11\)
2. \(5x-8\le 17\)
3. \(\dfrac{x}{3}+2<6\)
4. \(4x+1\ge -11\)

8 Variables on both sides ★★★

Solve each inequality.

1. \(5x-7>2x+8\)
2. \(3(x+4)\le 2x+9\)
3. \(7-2x\ge 4x+25\)

9 All numbers or none ★★★

Solve each inequality and describe the solution set.

1. \(2(x+3)>2x+1\)
2. \(3x-5\le 3x-8\)
3. \(x+5\ge x+5\)

10 Spot the error ★★★

A student solves \(-2x+1>9\) like this: “Subtract 1: \(-2x>8\). Divide by \(-2\): \(x>-4\).” Find the mistake, give the correct answer, and graph it.

11 Compound with and ★★★

Solve and write each answer as a chain.

1. \(-7<3x-1\le 11\)
2. \(4\le -2x<10\)

12 Compound with or ★★★

Solve each compound inequality and graph part (a).

1. \(x+3<1\) or \(x-2\ge 5\)
2. \(2x>6\) or \(-x\ge 1\)

13 Absolute value equations ★★★

Solve each equation.

1. \(|x|=8\)
2. \(|x+3|=5\)
3. \(|3x-6|=12\)
4. \(|2x+1|=-4\)

14 Absolute value inequalities ★★★

Solve each inequality.

1. \(|x|<6\)
2. \(|x|\ge 4\)
3. \(|x-2|\le 3\)
4. \(|x+1|>2\)

15 School supplies budget ★★★

Mia has $60 to spend. She has already spent $22.50, and each notebook costs $3.75. Write and solve an inequality to find how many more notebooks she can buy.

16 Fractions and decimals ★★★

Solve each inequality.

1. \(\dfrac{2x-1}{3}-\dfrac{x+2}{4}\ge 1\)
2. \(0.4x+1.2<0.1x-0.9\)

17 Harder absolute equations ★★★

Solve each equation.

1. \(3|2x-1|+4=19\)
2. \(|3x-2|=|x+6|\)
3. \(|5-2x|=7\)

18 Harder absolute inequalities ★★★

Solve each inequality.

1. \(2|x-4|+3<11\)
2. \(-3|x+1|\le -12\)
3. \(|4x-3|-5>0\)

19 Bottle tolerance ★★★

A machine fills bottles with 500 milliliters (mL) of juice. Each bottle must be within 6 mL of the target. (a) Write an absolute value inequality for the volume \(v\). (b) Solve it. (c) Is a bottle of 507 mL acceptable? (d) Convert the limits to U.S. fluid ounces (1 mL \(\approx\) 0.0338 fl oz).

20 Reaching a test average ★★★

Jordan’s first four test scores are 82, 90, 78, and 88. The maximum score is 100. What must the fifth score \(s\) be for the average of all five tests to be at least 85?

21 Bakery profit ★★★

A bakery sells muffins for $2.75 each. The ingredients cost $1.10 per muffin, and the weekly fixed costs are $120. How many muffins must be sold in a week to earn a profit of at least $300?

22 Comparing two plans ★★★

Plan A costs a flat $12 a month for movies. Plan B costs $4 a month plus $1.60 per movie. (a) For how many movies is Plan B cheaper? (b) For how many movies is it the same price? Graph the answer to (a).