Unit 4 Skill 3 - Inequalities

Which inequality is graphed here?

• -2 > x > 7

• -2 ≥ x ≥ 7

• 7 > x > -2

• 7 < x < -2

Answer explanation

The graph shows the region between -2 and 7, indicating that x is greater than -2 and less than 7. This corresponds to the inequality 7 > x > -2, which is the correct choice.

Match the graph with its inequality.

• b > –2

• b < –2

• b ≥ –2

• b ≤ –2

Answer explanation

The graph shows a solid line at -2, indicating that -2 is included in the solution set. This corresponds to the inequality b ≤ -2, meaning b can be less than or equal to -2.

What inequality is shown?

• x ≥ 0 OR x < 5

• 0 ≤ x ≤ 5

• 0 ≤ x < 5

• 0 ≥ x > 5

Answer explanation

The correct inequality is 0 ≤ x < 5, which indicates that x can take any value from 0 up to, but not including, 5. This matches the choice that specifies both lower and upper bounds for x.

Pick the correct letter for:
6 > x

• A

• B

• C

• D

Answer explanation

The inequality 6 > x means x must be less than 6. The correct choice is B, which represents a value less than 6.

Solve.

10 ≥ x - 3

• x ≤ 13

• x ≥ 13

• x ≤ 7

• x ≥ 7

Answer explanation

To solve 10 ≥ x - 3, add 3 to both sides: 13 ≥ x. This can be rewritten as x ≤ 13, which matches the correct answer choice.

5z - 2 - 2z < 13

• z > 5

• z < 5

• z > 1

• z < 1

Answer explanation

To solve the inequality 5z - 2 - 2z < 13, simplify to 3z - 2 < 13. Adding 2 gives 3z < 15, and dividing by 3 results in z < 5. Thus, the correct answer is z < 5.

Solve:
3(x - 2) < 2(x + 9)

• x<24

• x>12

• x<12

• x>24

Answer explanation

To solve 3(x - 2) < 2(x + 9), first distribute: 3x - 6 < 2x + 18. Then, subtract 2x from both sides: x - 6 < 18. Adding 6 gives x < 24. Thus, the correct answer is x < 24.

Your family needs 2 gallons of water this week, but you don’t want to buy any more than 8 gallons. Write an inequality representing the possible gallons of water you could buy this week.

• 2 ≤ x ≤ 8

• 2< x < 8

• 8 ≥ x ≥ 2

• 2> x > 8

Answer explanation

The family needs at least 2 gallons and no more than 8 gallons. This is represented by the inequality 2 ≤ x ≤ 8, meaning x can be any value from 2 to 8, inclusive.

At the local 5k race, runners 10 and under or runners 65 and above start the race after the others. What compound inequality represents the situation?

• 10 ≤ x ≤ 65

• x ≥ 10 or x ≤ 65

• x ≤ 10 or x ≥ 65

• 10 < x < 65

Answer explanation

The correct choice is x ≤ 10 or x ≥ 65, as it indicates that runners 10 and under (x ≤ 10) and runners 65 and above (x ≥ 65) start after the others, capturing both age groups.

Assuming a - b > c is true, which of the following inequalities is equivalent (i.e. means the same thing)?

• b > x - z

• b > c + a

• b > c - a

• b > c/a

Answer explanation

Starting from -b > c, we can rearrange it to b < -c. Adding a to both sides gives b < -c + a, which simplifies to b > c - a. Thus, the equivalent inequality is b > c - a.