Chapter 5

Chapter 5

Mindy’s empty suitcase weighs 8 pounds. The airline allows luggage to weigh no more than 40 pounds.

Write an inequality that shows the total weight w of the items Mindy can pack in her suitcase.

8 + w ≤ 40

You may have use an incorrect inequality symbol. you may not understand the phrase no more than.” Ask yourself if a weight of exactly 40 pounds is acceptable. Then ask if 39 pounds or 41 pounds is acceptable.

Solve the inequality

3p > -6 + p

Write the compound inequality shown on the

graph.

If you write an OR inequality, may not understand that when OR is used, only one of the conditions needs to be met. When AND is used, both conditions must be met. Do you think that whether the point -6 satisfies the OR inequality or if -6 satisfies the AND inequality.

Solve the inequality, and graph its solution.

-1/2a ≤ 2

Don't forget to reverse the inequality symbol when multiplying by a negative number. Review why this must be done, and check your answer by testing different values.

On Tuesday, the high temperature was 79°F, and the low temperature was 56°F. Write a compound inequality that represents the possible temperatures t on that day.

56 ≤ t ≤ 79

Solve the inequality, and graph its

solution

3c + 1 < 7 OR c - 5 ≥ -1

9 ≤ m ≤ 20

Solve the inequality.

-9 ≤ x - 4 < 1

a - 5 < 5

6(z - 1) ≤ -6

-2x > 0

b - 3 < -3 OR 5b ≤ -10

You should write the inequality shown on the graph. Then you should simplify each inequality answer choice. After simplifying, should compare each answer choice to the inequality you wrote for the graph.

What is the solution to the inequality?

4(x + 1) ≥ 5x + 7

Graph the solution to y ≤ 3x.

Write an inequality that shows the number of pens p that Javier can buy.

• 6.25 + 0.30p ≤ 10

Solve the inequality. Explain each step.

• 0.30p ≤ 3.75; subtract 6.25 from each side.

• p ≤ 12.5; divide each side by 0.30.

Graph the solution to -3x + 3y + 7 > 13.

You should read the problem carefully, underlining important information. Since the table shows prices that are not needed, students should circle the relevant information.

Solve -3(x + 1) ≤ x + 5. Show your work and explain each step. Graph the solution.

• -3x - 3 ≤ x + 5; Distributive Property

• -4x - 3 ≤ 5; subtract x from both sides.

• -4x ≤ 8; add 3 to both sides.

• x ≥ -2; divide each side by -4 and reverse the inequality sign.

Whoever answer incorrectly may not have correctly used the Distributive Property. Review how to distribute the -3 to each term in the parentheses.

Jocelyn said that she was thinking of a number and that the number satisfied two inequalities:

4x - 7 ≥ x + 14 and -x - 20 ≤ -3x - 6. What was Jocelyn’s number? Explain.

• 7

• the solution to the first inequality is x ≥ 7, and the solution to the second inequality is x ≤ 7.

• The only number that satisfies both is 7.