Two Step Inequalities

Two-Step Inequalities

Vocabulary Review

• > = Greater Than

• ≥ = Greater Than or Equal To

• < = Less Than

• ≤ = Less Than or Equal To

Greater Than or Equal To

• At least

• No less than

• A minimum of

Less Than or Equal To

• At most

• No more than

• A maximum of

Multiple Select

John goes to school less than five times a week. This value can be modeled with the following inequality:

• x > 5

• x ≤ 5

• x < 5

• x ≥ 5

Multiple Select

Steph spends at least $44.11 at the store. The amount spent can be modeled with the following equation:

• x > $44.11

• x ≤ $44.11

• x ≥ $44.11

• x < $44.11

Multiple Select

Alex will chew no more than seventy-seven sticks of gum this year. This value can be modeled with the following equation:

• x ≥ 77

• x ≥ 7

• x ≤ 7

• x ≤ 77

Multiple Select

Ms. Q has more than six children. This value can be modeled with the following inequality:

• x > 6

• x < 6

• x ≤ 6

• x ≥ 6

Steps to solve a two-step inequality:

• 1. I will be able to identify the parts of an inequality.

• 2. I will be able to solve an inequality.

Multiple Select

What values of x make the following inequality true?

4x + 5 > 9

• x > 1

• x < -1

• x > -1

• x < 1

Multiple Select

What values of x make the following inequality true?

6x + 24 ≤ 36

• x > 2

• x ≥ 2

• x ≤ 2

• x > -2

Multiple Select

What values of x make the following inequality true?

8x - 41 < 23

• x > 7

• x ≥ 8

• x ≤ -8

• x < 8

Multiple Select

What values of x make the following inequality true?

5x + 7 ≥ -8

• x ≥ -2

• x ≥ -2

• x > -2

• x < -2

Multiple Select

Greg is a handyman who charges $40 for a visit and $10 per hour for labor. He made a visit on Sunday that cost at least a total of $110. The equation can be modeled with the inequality 10h + 40 ≥ 110, where h is the number of hours he worked. Which of the following inequalities represent all possible values of h?

• h > 0

• h ≥ 0

• h ≥ 7

• h > 7

Multiple Select

Josephina is buying lunch for a group of three people. Josephina has a coupon for $20 off the total bill and wants to spend less than $52 after using the coupon. The inequality 3p － 20 < 54 can be used to find p, the average price of each person's lunch. Solve the inequality.

• p > 14

• p < 14

• x < 14

• p > 3

Multiple Select

What values of u make the inequality true?

3.3u + 10.1 < 20

• u > 4

• u < -3

• u < 10

• u < 3

Multiple Select

What values of u make the inequality true?

3.3u + 10.1 < 20

• u > 4

• u < -3

• u < 10

• u < 3