Solving Inequalities

● Solving inequalities follows the same procedures as solving equations.

● There are a few special things to

consider with inequalities:● We need to look carefully at the inequality sign.● We also need to graph the solution set.

Review of Inequality Signs

> greater than

< less than< less than

greater than or equal

less than or equal

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

Solve the inequality:

x + 4 < 7 -4 -4

x < 3

●Subtract 4 from each side.

●Keep the same inequality sign.

●Graph the solution.

• Open circle, line to the left.

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Can we always undo and keep the inequality true?

Let’s investigate: 2 < 6 Adding to both sides? 2 + 2 < 6 + 2 Subtracting on both sides? 2 – 2 < 6 - 2

Let’s investigate: 2 < 6 Multiply both sides? 2 ∙ 2 < 6 ∙ 2 Dividing on both sides? 2 2 < 6 2

Can we always undo and keep the inequality true?

So far so good?

What about multiplying and dividing by a negative number?:

2 < 6 Multiply both sides by -2? 2 ∙ -2 < 6 ∙ -2 If we multiply or divide by a

negative number we need to flip the inequality sign.

There is one special case.

● You only reverse the inequality sign when when you multiply or divide both sides of the inequality by a negative number.

Example:

Solve: -3y + 5 >23

-5 -5

-3y > 18

-3 -3

y < -6

●Subtract 5 from each side.

●Divide each side by negative 3.

●Reverse the inequality sign.

●Graph the solution.

•Open circle, line to the left.

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Try these:

● Solve 2x+3>x+5

● Solve - c - 11>23

● Solve 162)2(3 rr

Homework:

● Pg 572 #2 to 12 even● Pg. 572 #22 to 30 even● Pg. 573 #2 to 16 even