Warm-Up

Graphing Inequalities

SCOS 4.01

ObjectiveThe student will be able

to:1. graph inequalities on a

number line.2. solve inequalities using

addition and subtraction.

Designed by Skip Tyler, Varina High School

Symbols and MeaningsEqualities Inequalities

=Equals- is the same as

Congruent- same size and shape

Similar- same shape

< Is less than

> Is greater than

Is less than or equal to

Approx. equal to

= Not equal to

~

Is greater than or equal to

Not Equal

Graphing Symbols

Decide whether 4 is a solution of the inequality.

2x 1 8

x 4 9

x 3 1

2 4 1 8 7< 8 True 4 is a solution

4 4 9 8> 9 False, 4 is not a solution

4 3 1 1 1 True, 4 is a solution

Checking Solutions of Equations

When you graph inequalities that have only one variable, we use a number line. We will use open and closed circles and arrows pointing to the left or right to graph our answers. Take a look at the model below.

x<-3

1) Graph the solution set of

x < 3.

When you have < or >, use an open dot!

0 5-5o

2) Graph the solution set of

y ≥ -5/4.

When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

0 5-5 •

3) Graph the solution set of

p ≠ 2.

When you have ≠, use an open dot and shade both ways!

0 5-5o

White Board 1-6

White Board 7-12

White Board 13-18

Write an inequality

Write an inequality

Write an inequality

Write an inequality

4) Which inequality would have a closed dot on the number line?

1. >2. <3. ≥4. ≠

Answer NowAnswer Now

5) Which inequality does NOT use an open dot on the number line?

1. ≤2. <3. >4. ≠

Answer NowAnswer Now

6) Solve x + (-14) < 16 x - 14 < 16 + 14 + 14

x < 30

30 + (-14) = 1616 = 16

Solve this problem like an equation

1. Draw “the river”2. Eliminate double

signs3. Add 14 to both sides4. Simplify5. Check your answer6. Graph the solution

o30 3129

7) Solve y + 21 ≥ 7 - 21 -21 y ≥ -14

(-14) + 21 = 7

7 = 7

1. Draw the “river”2. Subtract 21 from

both sides3. Simplify4. Check your answer5. Graph the solution

-14 -13-15●

8) Solve 8y + 3 > 9y - 14

1. Draw “the river”2. Subtract 8y from

both sides3. Simplify4. Add 14 to both

sides5. Simplify6. Rewrite inequality

with the variable first

7. Check your answer8. Graph the solution

o17 1816

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

y < 178(17) + 3 = 9(17) - 14

9) What is the graph of 7 ≤ m?

1.

2.

3.

4.

o7 86o7 86●7 86

7 86●

Answer NowAnswer Now

10) Solve 3r - 17 ≥ 2r + 14

●31 3230

- 2r - 2r

r – 17 ≥ 14

+ 17 + 17

r ≥ 31 3(31) - 17 = 2(31) + 14

1. Draw “the river”

2. Subtract 2r from both sides

3. Simplify

4. Add 17 to both sides

5. Simplify

6. Check your answer

7. Graph the solution

11) Solve -2x + 6 ≥ 3x - 41. x ≥ -2

2. x ≤ -23. x ≥ 24. x ≤ 2

Answer NowAnswer Now

12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a

total of at least 459?1. 962. 973. 984. 100

Answer NowAnswer Now

Your scores on the last three tests were 82, 87, and 74. Your score on the next test is x points. Do the following values for x give you at least 320 total points?

a. 75 points b. 81 points

No Yes