Solving Inequalities: math practice, Grade 7 – download the PDF

1 Words to symbols ★★★

Write each statement as an inequality.

1. \(y\) is less than 9.
2. \(n\) is at most 12.
3. \(p\) is more than 3.
4. \(t\) is no less than \(-2\).

2 True or false? ★★★

Decide whether each statement is true or false.

1. \(3 \lt 7\)
2. \(-4 \gt -1\)
3. \(-5 \le -5\)
4. \(0 \gt -2\)
5. \(-8 \lt -9\)

3 Is it a solution? ★★★

For the inequality \(x + 4 \gt 10\), decide whether each value is a solution: 5, 6, 7, 12.

4 One-step with addition ★★★

Solve each inequality.

1. \(x + 5 \gt 12\)
2. \(x - 3 \le 4\)
3. \(6 \le x + 1\)

5 One-step with multiplication ★★★

Solve each inequality.

1. \(3x \lt 18\)
2. \(\dfrac{x}{4} \ge 2\)
3. \(5x \gt -20\)

6 Graph it ★★★

Graph the solution set of \(x \gt 2\) on a number line. Explain your choice of circle.

7 Read the graph ★★★

Write the inequality shown by this graph, then name two solutions and one number that is not a solution.

8 Two-step inequalities ★★★

Solve each inequality.

1. \(2x + 3 \gt 11\)
2. \(5x - 7 \le 18\)
3. \(4x + 1 \lt -11\)

9 Dividing by a negative ★★★

Solve each inequality and flip the sign when needed.

1. \(-2x \lt 10\)
2. \(-3x \ge 12\)
3. \(\dfrac{x}{-5} \gt 2\)

10 Bike rental budget ★★★

A bike shop charges a 6-dollar fee plus 2.50 dollars per hour. Lena has 21 dollars. Write and solve an inequality for the number of hours \(h\) she can rent the bike, and interpret the answer.

11 Find the mistake ★★★

Marco solved \(-4x \gt 20\) and wrote \(x \gt -5\). Test his answer with \(x = 0\) and with \(x = -10\), find his error, and give the correct solution set.

12 Negative coefficient first ★★★

Solve each inequality.

1. \(7 - 2x \gt 1\)
2. \(10 - x \le 4\)

13 Elevator limit ★★★

A freight elevator can carry at most 1,200 pounds (about 544 kg). A crate weighs 150 pounds and each box weighs 45 pounds. Write an inequality for the number of boxes \(n\) that can ride with the crate, solve it, and state the greatest number of boxes.

14 Saving for a laptop ★★★

Mia has 85 dollars and saves 12 dollars each week. She wants at least 200 dollars for a laptop. After how many whole weeks \(w\) can she buy it?

15 Warming a pool ★★★

A pool is at 70°F (about 21°C) and a heater raises it by 2°F each hour. The water must be warmer than 78°F. Write and solve an inequality for the time \(t\) in hours, then graph it.

16 Distribute first ★★★

Solve each inequality.

1. \(3(x - 2) + 5 \lt 20\)
2. \(2(4 - x) \ge 14\)

17 Fractions in inequalities ★★★

Solve each inequality.

1. \(\dfrac{2}{3}x - 4 \ge 6\)
2. \(-\dfrac{1}{2}x + 3 \lt -1\)

18 Variables on both sides ★★★

Solve each inequality.

1. \(5x + 2 \gt 3x + 10\)
2. \(7x - 4 \le 4x + 11\)

19 Two conditions at once ★★★

A whole number \(x\) satisfies both \(2x - 1 \gt 5\) and \(x \lt 8\). Solve the first inequality, graph the combined solutions on a number line, and list all possible whole numbers.

20 Food truck profit ★★★

A food truck pays 240 dollars per day to operate. Each meal sells for 8 dollars and costs 3 dollars in ingredients. Write an inequality for the number of meals \(n\) needed to make a profit (more than 0), solve it, and state the smallest number of meals.

21 Draining a tank ★★★

A tank holds 90 gallons (about 340 liters) and drains at 6 gallons per minute. After \(m\) minutes, for how long must it drain so that fewer than 30 gallons remain? Solve and interpret.

22 Always, sometimes, never ★★★

For each inequality, say whether it is true for all numbers, some numbers, or no numbers, and explain.

1. \(x + 1 \gt x\)
2. \(x \gt x + 1\)
3. \(2x \gt x\)