Inequalities

Graphing

100

Graph the inequality on a number line.

x > -10

Graph should have an open dot at -10 with an arrow pointing to the right (towards zero)

200

Graph the inequality on a number line.

y ≤ 0.5

Graph should have a closed dot at 0.5 with an arrow pointing to the left (towards the negatives)

300

Graph the inequality on a number line.

15 ≤ k

Graph should have a closed dot at 15 with an arrow pointing to the right (towards larger numbers)

400

Graph the inequality on a number line.

-33 > p

Graph should have an open dot at -33 with an arrow pointing to the left (away from zero)

500

Graph the inequality on a number line.

8x ≥ -96

Graph should have a closed dot at -12 with an arrow pointing to the right (towards zero)

Writing Inequalities

100

Write an inequality to represent this situation:

You have to be at least 24 years old in order to rent the car.

a ≥ 24

200

Write an inequality to represent this situation:

The temperature outside is colder the -2 degrees.

t < -2

300

Write an inequality to represent this situation:

You can spend at most $57.25 at the mall.

m ≤ 57.25

400

Write an inequality to represent this situation:

The difference between 2n and 7 is less than or equal to 40.

2n - 7 ≤  40

OR

n ≤ 23.5

500

You pay $24 to get into the fair, then spend $5 on each game you play while inside. You brought $65 with you. Write an inequality that represents how much money you spend.

5g + 24 ≤ 65

OR 

5g ≤ 41

OR

g ≤ 8.2

Is it a solution?

100

18.2 > p

Is 18.3 a solution to the inequality?

No, 18.2 is not > 18.3

200

y  ≥ -75

Is -85 a solution to this inequality?

No, -85 is not  ≥  -75

300

m ≤ -0.7

Is -0.75 a solution to the inequality?

Yes, -0.75 ≤ -0.70

400

2y + 3 < 7

Is 0 a solution to the inequality?

Yes, 3 < 7

2(0) + 3 = 3

500

-12 < -5(x + 13)

Is -11 a solution to the inequality?

Yes, -12 < -10

-5( -11 + 13) = -5(2) = -10

Solving Inequalities

100

Solve the inequality for x.

x + 3 > -10

x > -13

200

Solve the inequality for m.

-15 ≤ 3m

-5 ≤ m

OR

m ≥ -5

300

Solve the inequality for a.

-7 + a ≤ -30

a ≤ -23

400

Solve the inequality for c.

-22.45 > c - 26.3

3.85 > c

OR

c < 3.85

500

Solve the inequality for y.

-3y + 4y + 10y ≥ -852 + 82

y ≥ -70

Solving Multi-Step Equations (review)

100

Solve for x.

3x + 7x - 2 = 74 + 4

x = 8

200

Solve for k.

-12 = -3(k + 9)

k = -5

300

Solve for y.

-5y + 4 = 2y + 10 + 15

y = -3

400

Solve for g.

-(-2g + 8) = 2(4g - 4)

g = 0

(No, it is not no solution)

500

Solve for f.

-f - 17 + 10f = 0.5(18f - 34)

Infinite Solutions