Inequalities

One-Step

100

1) Solve for p:

9p<-81

p<-9

200

3) Solve for c:

^c/₂ ≤ -0.75

c ≤ -1.5

300

5) Solve for x:

10 - x ≤ 35

x ≥ -25

Two-Step

100

7) Solve for x:

30 < 2x - 6

x > 18

200

8) Solve for x:

1.5x + 12 < 18

x < 4

300

9) Solve for x:

16 ≥ 6 + ^x/₂

x ≤ 20

Graph

100

11) x < 4.5

<--|---|---|---|---ϕ---|---|---|---|--->

      ^{2.5    3     3.5    4   4.5    5    5.5    6     6.5}

200

13) Graph

 ⁴/₅ > x

<--|---|---|---|---ϕ---|---|---|---|--->

      ^{0    1/5   2/5   3/5  4/5   1    6/5  7/5  8/5}

300

15) Graph

7x + 22 ≤ 15

<--|---|---|---|---ϕ---|---|---|---|--->

       ^{-5    -4    -3     -2    -1      0     1     2     3}

Write or correct inequalities

100

10) Eduardo solved the inequality below. Did he solve the problem correctly? If not, explain his mistake or show the correct answer.

No, he forgot to divide by negative 4 and forgot to change the inequality sign.

x ≤ 4

200

16) Jasmine has a budget of $600 to spend on home renovations. She will spend $175 on a new sink and the remainder on countertops. The countertops cost $35 per square foot. What is the maximum number of square feet Jasmine can purchase?

Variable: _______________

Inequality: _____________________

Variable: s = number of square feet

Inequality: 35s+175≤600

300

18) Russell wants to buy three ties and a belt and cannot spend more than $80. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie?

Variable: t=tie price

Inequality: 3t + 28.5 ≤ 80

Real-World Inequalities

100

19a) Determine whether the inequality below correctly represents the situation. If so, write "yes" in not write the correct inequality.

12 + 1.50x ≤ 60

An online music service charges $12 registration fee, plus $1.50 for each song downloaded. If Mary Beth has a gift card with $60, then how many songs can she download?

YES, this is representative

200

19b) Determine whether the inequality below correctly represents the situation. If so, write "yes" in not write the correct inequality.

12 + 1.50x ≤ 60

A construction company is building a retaining wall. It has a 12-inch piece of stone and then bricks are stacked on top. Each brick measures 1.5 inches in height and the entire wall must be a least 60 inches tall. How many rows of bricks will the retaining wall have?

12 + 1.50x ≥ 60

300

22) A 15-passenger van is rented for a family vacation. The van rental is $60 per day, plus a $145 insurance fee. How many days can the van be rented if the family wants to spend no more than $625 on the van rental? Write and solve an inequality.

Inequality: 60d + 145 ≤ 625

Solution: d ≤ 8