Solving Compound Inequalities, Exercises of Linear Algebra

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Notes 6.

Solving

Compound

Inequalities

I. Compound Inequalities

• Compound inequalities are two inequalities that

are graphed on the same number line and have

either an ‘and’ or an ‘or’ relationship

A. Definition

1) Graph x < 4 and x ≥ 2

●

a) Graph x < 4

b) Graph x ≥ 2

o

c) Combine the graphs

●

o

d) Where do they intersect?

● 2 3 4

o

II. Examples

2) Graph x < 2 or x ≥ 4

●

a) Graph x < 2

b) Graph x ≥ 4

o

c) Combine the graphs

o

o

●

3) Which inequalities describe the

following graph?

1. y > - 3 or y < - 1
2. y > - 3 and y < - 1
3. y ≤ - 3 or y ≥ - 1
4. y ≥ - 3 and y ≤ - 1

o o

Answer Now

III. Graph the compound inequality

6 < m < 8

When written this way, it is the same thing as

6 < m AND m < 8

It can be rewritten as m > 6 and m < 8 and

graphed as previously shown, however,

it is easier to graph everything

between 6 and 8!

o o

6) Which is equivalent to

x > - 5 and x ≤ 1?

1. - 5 < x ≤ 1

2. - 5 > x ≥ 1

3. - 5 > x ≤ 1

4. - 5 < x ≥ 1

Answer Now

7) 2x < - 6 and 3x ≥ 12

1. Solve each inequality

for x

2. Graph each inequality
3. Combine the graphs
4. Where do they

intersect?

5. They do not! x cannot

be greater than or equal to 4 and less than - 3 No Solution!!

x

x

3x 12

x 4

o

o

●o 1 4 7

●o

• 9. Graph x < 2 or x ≥
• • 50

10. Graph x ≥ - 1 or x ≤ 3

The whole line is shaded!!

-5 0 5