3.5 Compound Inequalities

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# 3.5 Compound Inequalities - PowerPoint PPT Presentation

3.5 Compound Inequalities. Objective: SWBAT solve compound inequalities. Mini Quiz 24. 1. Solve 2 x – 3 ≤ 5 x + 9 2. Solve 2 x – 4 ≤ 2(3 x – 6) 3. Is -2 a solution to the inequality x – 2 ≤ 5(x-1). Quick Review. 1. Evaluate |-4| 4 2. True or False: |-5| = -5 False

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### 3.5 Compound Inequalities

Objective: SWBAT solve compound inequalities.

Mini Quiz 24

1. Solve 2x – 3 ≤ 5x + 9

2. Solve 2x – 4 ≤ 2(3x – 6)

3. Is -2 a solution to the inequality

x – 2 ≤ 5(x-1)

Quick Review

1. Evaluate |-4|

4

2. True or False: |-5| = -5

False

3. What two values can x equal for the equation |x| = 8

-8, 8

4. What is the distance of 3 and -2?

5

Compound Inequality

Compound Inequality - two inequalities connected by andor or(this is similar to compound sentences in English, which are joined by and, or, or but).

Example:

0 < x ≤ 4 (aka 0 < x and x ≤ 4)

x < -1 or x > 2 (or can’t be combined)

Note: it’s one way OR the other

0

0

Compound Inequality with “OR”

Solve and graph the solution

1. 3x + 1 < 4 or 2x – 5 > 7

3x < 3 or 2x > 12

x < 1 or x > 6

0

Compound Inequality with “AND”

Solve and Graph

2. -2 ≤ 3x – 8 ≤ 10

Method 1: Method 2:

-2 ≤ 3x – 8 ≤ 10 -2 ≤ 3x – 8 and 3x – 8 ≤ 10

+8 + 8 +8 +8 + 8 +8 +8

6 ≤ 3x ≤ 18 6 ≤ 3x and 3x ≤ 18

3 3 3 3 3 3 3

2 ≤ x ≤ 6 2 ≤ x and x ≤ 6

2 ≤ x ≤ 6

0

Solving Compound Inequalities with “AND” and “OR”

Solve and Graph the inequalities

3. –2 < -2 – x < 1

0 > x > -3

0

Solving Compound Inequalities with “AND” and “OR”

Solve and Graph the inequalities

4. 2x + 3 < -1 or 3x – 5 > -2

x < -2 or x > 1

0

Solving Compound Inequalities with “AND” and “OR”

Solve and Graph the inequalities

5. 7 < 4 + x < 8

3 < x < 4

0

Solving Compound Inequalities with “AND” and “OR”

Solve and Graph the inequalities

6. -1 < 2x + 3 ≤ 13

-2 < x ≤ 5

0

Solving Compound Inequalities with “AND” and “OR”

7. 4x – 1 > 7 or 5x – 1 < -6

x < 2 or x < -1

0

Wrap Up

Compound Inequalities

• OR - solve each one separately
• AND – isolate variable or break into two problems and solve each one separately