Solving Compound Inequalities

Domain: A-REI Reasoning with Equations & Inequalities

Cluster: 1. Understand solving equations as a process of reasoning and explain the reasoning.

Standard 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Domain: A-REI Reasoning with Equations & Inequalities

Cluster: 2. Solve equations and inequalities in one variable.

Standard: 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

What is the difference between “and” and “or”?

AND means intersection-only elements common to

both sets are part of the solution.

OR means union-Elements from both sets

are part of the solution.

A

A B

B

1. Graph x < 4 and x ≥ 2

3 42●

a) Graph x < 4

b) Graph x ≥ 23 42

o

●

3 42o

c) Where do they intersect?

●3 42

o

2. Graph x < 2 or x ≥ 4

3 42●

a) Graph x < 2

b) Graph x ≥ 43 42

o

c) Unite the graphs

3 42o

3 42●

3. Which inequalities describe the following graph?

A. y > -3 or y < -1B. y > -3 and y < -1

C. y ≤ -3 or y ≥ -1D. y ≥ -3 and y ≤ -1

-2 -1-3oo

Can also be written as:

-3 < y < -1

4. Graph the compound inequality 6 < m < 8

7 86oo

“6 is less than m and m is less than 8”

6 7 8

6 7 8

o

o

“m is between 6 and 8”

5. Which is equivalent to-3 < y < 5?

A. y > -3 or y < 5B. y > -3 and y < 5C. y < -3 or y > 5D. y < -3 and y > 5

0 5-3oo

6. Which is equivalent to x > -5 and x ≤ 1?

A. -5 < x ≤ 1B. -5 > x ≥ 1C. -5 > x ≤ 1D. -5 < x ≥ 1

o0 1-5

7. Solve: 2x < -6 and 3x ≥ 12

1. Solve each inequality

1. Graph each solution

1. Where do they intersect?

1. They do not! No Solution!!

2 6

2 2 3

x

x

3x 12

3 3 x 4

-3 0-6o-3 0-6o

4 71o●4 71o●

8. Solve:3x+2 < 2 or 1-x ≥ 4

0 5-3

0 1-1o

-3 -2-4●

Unite the two sets

o ●

10. Graph x > -1 or x < 3

The entire number line is shaded!!

What is the solution???

All Real Numbers

0 3-1

10. Solve: 3 < 2m – 1 < 9

0 5-5

See Next Slide for Different Method.

Find the intersectionof the two sets.

10. Method 2:

0 5-5