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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.7.EE.B.4B

 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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.6.EE.B.8

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.

Tags

CCSS.7.EE.B.4B

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.

Tags

CCSS.7.EE.B.4B