Unit 5 Inequalities Review

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Answer explanation

To find the number of miles, x, the driver needs to drive, we set up the inequality: rental fee ($375) plus the cost per mile ($0.85x) must be greater than $450. Thus, the correct inequality is 0.85x + 375 > 450.

Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.

Which inequality could help you find how many dogs Katie would have to walk to reach her goal?

• 25 - 12x ≥ 200

• 25 + 12x ≥ 200

• 13x ≥ 200

• 25 + 12x < 200

Answer explanation

To find how many dogs Katie needs to walk, we start with her current amount ($25) and add the money she earns from walking dogs ($12 per dog). The inequality 25 + 12x ≥ 200 represents this situation.

Solve:

• x < 24

• x < 3

• x > 24

• x < 10.3333....

Answer explanation

To solve the inequality, we find that x must be less than 24. This is the only option that satisfies the condition, making 'x < 24' the correct answer.

Which of the following is the solution of  2x + 3 ≤ 9 in real numbers?

• x ≤ 3

• x ≥ 2

• x ≤ 6

• x < 6

Answer explanation

To solve 2x + 3 ≤ 9, subtract 3 from both sides to get 2x ≤ 6. Then, divide by 2 to find x ≤ 3. Thus, the correct solution is x ≤ 3.

 Match the graph with the given solution.

• A

• B

• C

• D

Answer explanation

Graph B correctly represents the solution provided, aligning with the characteristics and data points outlined in the question. The other options do not match the required criteria.

Which graph matches the inequality
r ≥ -6?

• A

• B

• C

• D

Answer explanation

The inequality r ≥ -6 means r can be any value greater than or equal to -6. Graph A correctly shows a solid line at -6, indicating that -6 is included, and shading to the right, representing all values greater than -6.

Answer explanation

To solve the inequality 3x - 5 < 7, add 5 to both sides to get 3x < 12. Then, divide by 3 to find x < 4. Thus, the correct answer is x < 4.

Answer explanation

The inequality x ≥ -2 means x can be -2 or any number greater than -2. Therefore, we use a closed circle at -2 to indicate that -2 is included, and a line extending to the right to show all numbers greater than -2.

Write an inequality for the following word problem: "A number decreased by 4 is less than 10."

Answer explanation

The phrase 'A number decreased by 4' translates to 'x - 4'. The statement 'is less than 10' indicates a '<' relationship. Therefore, the correct inequality is x - 4 < 10.

Answer explanation

To solve the inequality -2x + 3 ≤ 7, subtract 3 from both sides to get -2x ≤ 4. Then, divide by -2, remembering to reverse the inequality sign, resulting in x ≥ -2. Thus, the correct answer is x ≥ -2.