SOLVE ABSOLUTE SOLVE ABSOLUTE VALUE INEQUALITIESVALUE INEQUALITIES

January 21, 2014January 21, 2014

Pages 398-400Pages 398-400

Do you remember???

1. Solve |x – 6| = 4.

2. Solve |x + 5| – 8 = 2.

ANSWER 2, 10

ANSWER –15, 5

Solve the inequality. Graph your solution.

1. – 6x >

The distance between x and 0 is greater than or equal to 6. So, x ≤ – 6 or x ≥ 6.

ANSWER

The solutions are all real numbers less than or equal to – 6 or greater than or equal to 6.

SOLUTION

2. < x 0.5 –

The distance between x and 0 is less than or equal to 0.5.So, to – 0.5 ≤ x ≤ 0.5.

SOLUTION

ANSWER

The solutions are all real numbers greater than or equal to – 0.5 and less than or equal to 0.5.

Solve the inequality. Graph your solution.

3. x 8<

SOLUTION

The distance between x and 0 is less equal to 8. So, – 8 ≤ x ≤ 8.

ANSWER

The solutions are all real numbers greater than or equal to – 8 and less than or equal to 8.

–9 –8 –7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9

. .

4. u < 3.5

SOLUTION

The distance between x and 0 is less or equal to 3.5. So, – 3.5 < u < 3.5.

ANSWER

The solutions are all real numbers greater than or equal to – 3.5 & less than or equal to 3.5.

..–4.5 –3.5 –2.5 –1.5 0 1.5 2.5 3.5 4.5

.

SOLUTION

The distance between x and 0 is less or greater

than so,23

23

23v < – or v >

33

– 23

33

13

23

– 13

– 0

ANSWER

The solutions are all real numbers greater than and less than

23–

23

5. v > 23

Solve x – 5 ≥ 7. Graph your solution.

Write original inequality.

x – 5 7<–

x – 5 7–>

or x – 5 7–> Rewrite as compound inequality.

x –2<– or –> x 12 Add 5 to each side.

ANSWER

The solutions are all real numbers less than or equal to – 2 or greater than or equal to 12. Check several solutions in the original inequality.

6.

Solve – 4x – 5 + 3 < 9. Graph your solution.

– 4x –5 + 3 < 9

–6 <–4x – 5 < 6

– 4x – 5 < 6

–1 <–4x < 11

0.25 > x > –2.75

–2.75 < x < 0.25

Write original inequality.

Subtract 3 from each side.

Rewrite as compound inequality.

Add 5 to each expression.

Rewrite in the form a < x < b.

Divide each expression by – 4. Reverse inequality symbol.

7.

ANSWER

The solutions are all real numbers greater than –2.75 and less than 0.25.

SOLUTION

Solve the inequality.

x + 3 > 88.

Write original inequality.

Rewrite as compound inequality.

Add – 3 to each side.

x + 3 > 8

or x + 3 < 8 x + 3 > 8

x < – 11 or x > 5

ANSWER

The solutions are all real numbers less than – 11 or greater than to 5 .

SOLUTION

2w – 1 < 119.

Write original inequality.

Rewrite as compound inequality.

Add 1 to each side.

2w – 1 < 11

or 2w – 1 > 11 2w – 1 < – 11

w < – 5 or w > 6 Divide by 2 to each side

ANSWER

– 5 < w <– 6

or 2w < – 10 2w > 12

SOLUTION

Write original inequality.

Divide by each side by 3.

Rewrite as compound inequality.

10. 3 5m – 6 – 8 13<–

3 5m – 6 – 8 13<–

Add 8 to each side.3 5m – 6 21<–

|5m – 6| 7<–

– 7 5m 6 7<– <–

– 1 ≤ 5m ≤ 13 Add 6 to each side.

– 0.2 ≤ m ≤ 2.6 Simplify.

The solutions are all real numbers greater than or equal to – 0.2 and less than or equal to 2.6 .

HOMEWORKHOMEWORK

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