4.1Solving Linear Inequalities

10/11/2013

Review of Inequality Signs

> greater than

< less than< less than

greater than or equal

less than or equal

Consider • Add 2 to both sides. >

• Subtract 2 from both sides. >

• Multiply both sides by 2. >

• Divide both sides by 2. >

• Multiply both sides by -2. <

• Divide both sides by -2. <

When did you change the direction of the inequality symbol?

Rule of InequalityWhen multiplying or dividing both sides of an inequality by a negative number, reverse the inequality symbol.

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

Example 1 Inequality with a Variable on One Side

Solve the inequality and graph the solution.

a. b.>x 4– 6– – ≥5y 2 13–+

SOLUTION

a. >x 4– 6–

>x 2–+ 4 + 4

b. – ≥5y 2 13–+

– ≥5y 15–

y ≤ 3

-2 -2

-5 -5

• Open circle, line to the right.• Closed circle, line to the left.

Reverse symbol

Example 2 Inequality with a Variable on Both Sides

Solve . Graph the solution.

<7 2x– 1

<7 4x 1 2x––

SOLUTION

<7 4x 1 2x––

<2x– 6–

>x 3

+2x +2x

-2 -2 Reverse symbol

• Open circle, line to the right.

- 7 -7

Checkpoint

Solve the inequality. Then graph your solution.

Solve an Inequality

<x 3 8+1.

5≤4 x–2.

ANSWER <x 5

210 3 4 5 6

ANSWER ≥x 1–

0 22–

Checkpoint

Solve the inequality. Then graph your solution.

– x>2x 34.

Solve an Inequality

2>2x 1–3.

3x >ANSWER

210 3 4 5 6

x >2

3ANSWER

1 20

Example 3 Word Problem

Amusement Park Admission to an amusement park costs $9 and each ride ticket costs $1.50. 1. Write an equation for the amount you’ll spend for

any given number of ride tickets you buy.2. If you only have $45, up to how many ride tickets

can you buy?

1 ticket2 tickets: 3 tickets: = 4 tickets: = x tickets:

You can buy up to 24 ride tickets.

ClassworkWorksheet 4.1Front page only

COMPOUND INEQUALITY2 simple inequalities joined by the word “and” or the word “or”. Ex: ANDAll real numbers greater than or equal to -2 and less than 1.

Ex: ORAll real numbers less than -1 or greater than or equal to 2

-2≤ x < 1

x < -1 or x ≥ 2

𝑥≥ −2 𝑥<1and is the same as

Note: The “shaded” part is in the middle of the 2 circled numbers.

Note: The “shaded” parts go in opposite direction from 2 circled numbers.

Example 4 Solve an “Or” Compound Inequality

Solve or3x + 2 8< 2x 9 3.– >

SOLUTION

Solve each part separately.

or

Example 5 Solve an “And” Compound Inequality

Solve

SOLUTION

Checkpoint

Solve the inequality. Then graph your solution.

Solve Compound Inequalities

5. 4 x< + 5 7<

ANSWER x 2<1 <–

2– 20

Checkpoint

Solve the inequality. Then graph your solution.

Solve Compound Inequalities

6. x + 3 4 or ≤ x 6– ≥ 1–

ANSWER x 1 or≤ x 5≥

420. .

7. 2x 6 0<– –x 4 or– >

ANSWER x 4 or–< x 3–>

06– 4– 2–

HomeworkWorksheet 4.1

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