Transcript

4.5

Compound Inequalities

4.5 – Compound Inequalities

• Goals / “I can…”– Solve and graph inequalities containing and– Solve and graph inequalities containing or

4.5 – Compound Inequalities

• A compound inequality is two inequalities joined with an and or an or.

AND (intersection)• The value for x makes BOTH inequalities true.

What is the difference between and and or?

AND means intersection-what do the two items

have in common?

OR means union-if it is in one item, it is in

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

c) Combine the graphs

3 42o

d) Where do they intersect?●

3 42o

2) Graph x < 2 or x ≥ 4

3 42●

a) Graph x < 2

b) Graph x ≥ 43 42

o

c) Combine the graphs

3 42o

3 42●

3 42●

4.5 – Compound Inequalities

Compound inequalities can be written as:

• -4 < x AND x < 5• -4 < x < 5

3) Which inequalities describe the following graph?

-2 -1-3oo

Answer NowAnswer Now

1. y > -3 or y < -12. y > -3 and y < -13. y ≤ -3 or y ≥ -14. y ≥ -3 and y ≤ -1

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!

4) Graph the compound inequality 6 < m < 8

7 86oo

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

1. y > -3 or y < 52. y > -3 and y < 53. y < -3 or y > 54. y < -3 and y > 5

Answer NowAnswer Now

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

1. -5 < x ≤ 12. -5 > x ≥ 13. -5 > x ≤ 14. -5 < x ≥ 1

Answer NowAnswer Now

7) 2x < -6 and 3x ≥ 12

1. Solve each inequality for x

2. Graph each inequality3. Combine the graphs4. Where do they

intersect?5. They do not! x cannot

be greater than or equal to 4 and less than -3 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) Graph 3 < 2m – 1 < 9

Remember, when written like this, it is an AND problem!

3 < 2m – 1 AND 2m – 1 < 9Solve each inequality.

Graph the intersection of 2 < m and m < 5.

0 5-5

9) Graph x < 2 or x ≥ 4

0 5-5

10) Graph x ≥ -1 or x ≤ 3

The whole line is shaded!!

0 5-5

4.5 – Compound Inequalities

Writing compound inequalities:• All real numbers that are less than 31 but

greater than 25.

4.5 – Compound Inequalities

• Graphing compound inequalities:- 4 < x < 5

4.5 – Compound Inequalities

Solving compound inequalities:• (Separate the inequalities)

5 > 5 – f > 2

4.5 – Compound Inequalities

OR (union)• The value for x makes one or the other

inequality true.

4.5 – Compound Inequalities

Writing OR• Discounted tickets are offered for children

under 7 or adults 65 and older.

• Graphing OR

4.5 – Compound Inequalities

Solving OR• (solve separately)

3x + 2 < -7 or - 4x + 5 < 1


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