Inequality SymbolsInequality Symbols

Less than

Greater than

Less than or equal to

Greater than or equal to

Not equal to

Name:Date:Period:

Topic: Solving Inequalities Essential Question: What is the correlation between solving equations and solving inequalities?

Warm-up: Name the following inequality signs:

An inequality is like an equation, but instead of an equal sign (=) it

has one of these signs:

Vocabulary:

Solving Inequalities

by

Adding or Subtracting

Solving the Inequality

w + 5 < 8

Note:

We will use the same steps that we did with equations, if a number is added to

the variable, we subtract the same number to both sides.

Answer

w + 5 < 8

w + 5 -5 < 8 -5

w + 0 < 3

w < 3 All numbers less than 3 are

solutions to this problem!

Now you try it!

8 + r ≥ -2

x - 2 > -2

4 + y ≤ 1

7 > x – 5

x + 2 ≤ 3

Answers to Practice Problems:8 + r ≥ -2

8 -8 + r ≥ -2 -8

r + 0 ≥ -10

w ≥ -10

All numbers from -10 and up (including

-10) make this problem true!

x - 2 > -2

x - 2 + 2 > -2 + 2

x + 0 > 0

x > 0

All numbers greater than 0 make this problem true!

4 + y ≤ 1

4 - 4 + y ≤ 1 - 4

y + 0 ≤ -3

y ≤ -3

All numbers from -3 down (including -3) make this problem

true!

Answers to Practice Problems: x - 5 > 7

x + 2 ≤ 3

x – 5 + 5 > 7 + 5

x + 0 > 12

x > 12

120

x + 2 - 2 ≤ 7 - 2

x + 0 ≤ 5

x ≤ 5

0 5

x < 5

What do these means?What do these means?

x ≤ 3

x > 4 x ≥ 2

How to graph the solutions

> Graph any number greater than. . .

open circle, line to the right

< Graph any number less than. . .

open circle, line to the left

Graph any number greater than or equal to. . .

closed circle, line to the right

Graph any number less than or equal to. . .

closed circle, line to the left

x < 5

x ≤ 3

x > 4

x ≥ 2

Solving Inequalities

by

Multiplying or Dividing

Solving the Inequality

< - 2

15b < 60

< - 2

15b < 60

Answers

x > 4

15b < 6015 15

b < 4

x < - 8

But wait there is one special case:

●Sometimes you may have to reverse the direction of the inequality sign!!

●That only happens when you multiply or divide both sides of the inequality by a negative number.

That was easy!!!

- 4r > 16

Solving the Inequality

Answers

(

((

(

m < - 10

- 4r > 16 - 4r > 16 - 4 - 4 r < - 4

Solving multi-step inequalitiesis like

solving multi-step equations.If you can solve

1132 xyou can solve

1132 x

1132 x 1132 x

Remember:

Which graph shows the solution to 2x - 10 ≥ 4?

Now you try it!Page 181 (1 – 4, 8, 16, 20)

1) 3(x + 4) - 5(x - 1) < 52) -2x + 6 ≥ 3x – 43) 3 (t + 1) – 4t ≥ - 54) 5m - 8 > 125) -5x – 9 < 26

Anytime you multiply or divide both sides of an

inequality by a negative number, you need to reverse

the sign.

Brief Review of InequalitiesBrief Review of Inequalities• Add/subtract the same number on each side of an inequality

• Multiply/divide by the same positive number on each side of an inequality

• If you multiply or divide by a negative number, you MUST flip the inequality sign!

Wrap-Up:

Home-Learning:

Page 175 (34), Page 176 (70),

Page 181 (12, 21, 24), Page 189 (2, 4),

Page 190 (20), Page 192 (59, 60)