Graphing, Writing and Solving Inequalities

1. graph inequalities on a number line.

2. solve inequalities using addition and subtraction.

ObjectiveThe student will be able to:

Graphing Inequalities

1) Graph the solution set ofx < 3.

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

0 5-5o

2) Graph the solution set ofy ≥ -5/4.

When you have ≤ or ≥, use a closed dot!

Converting -5/4 to a decimal = -1.25

0 5-5 •

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

1. >

2. <

3. ≥

Answer NowAnswer Now

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

1. ≤

2. <

3. >

Answer NowAnswer Now

Writing Inequalities from a Graph

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

+ 14 + 14

x < 30

30 + (-14) = 16

16 = 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

Solving Inequalities with Addition and Subtraction

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

o17 1816

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

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

1. Draw “the river”

2. Subtract 8y from both sides

3. Simplify

4. Add 14 to both sides

5. Simplify

6. Rewrite inequality with the variable first

7. Check your answer

8. Graph the solution

9) What is the graph of 7 ≤ m?

o7 86o7 86●7 86

7 86●

1.

2.

3.

4.

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 ≤ -2

3. x ≥ 2

4. 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?

Answer NowAnswer Now

1. 96

2. 97

3. 98

4. 100

Summation of Adding and Subtracting Inequalities