1.6 – Solving Compound and Absolute Value Inequalities

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

-7 -7

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

-7 -7

6

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

-7 -7

6 <

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

-7 -7

6 < 2x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17

-7 -7

6 < 2x

2 2

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3 <

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 6 < 2x 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x < 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x < 10 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x <

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x < 5

3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x < 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

0 3 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

0 3 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

0 3 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

0 3 5

1.6 – Solving Compound and Absolute Value Inequalities

Example 1 – Solve 13 < 2x + 7 ≤ 17 and graph the solution on a number line.

13 < 2x + 7 ≤ 17

13 < 2x + 7 2x + 7 ≤ 17 -7 -7 -7 -7 6 < 2x 2x ≤ 10 2 2 2 2 3 < x x ≤ 5

3 < x ≤ 5

0 3 5

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and graph the solution on a number line.

y – 2 > -3 or y + 4 ≤ -3

y – 2 > -3 or y + 4 ≤ -3

+2 +2 -4 -4

y > -1 or y ≤ -7

-7 -1 0

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

-4 0 4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

(b) Solve |a| > 4. Graph the solution on a number line.

-4 0 4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

(b) Solve |a| > 4. Graph the solution on a number line.

|a| > 4

-4 0 4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

(b) Solve |a| > 4. Graph the solution on a number line.

|a| > 4

a > 4 or a < -4

-4 0 4

Example 3

(a) Solve |a| < 4. Graph the solution on a number line.

|a| < 4

a < 4 or a > -4

(b) Solve |a| > 4. Graph the solution on a number line.

|a| > 4

a > 4 or a < -4

-4 0 4

-4 0 4

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

+12 +12 _ +12 +12

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

+12 +12 _ +12 +12

3x ≥ 18 3x < 6

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

+12 +12 _ +12 +12

3x ≥ 18 3x < 6

3 3 3 3

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

+12 +12 _ +12 +12

3x ≥ 18 3x < 6

3 3 3 3

x ≥ 6 x < 2

Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line.

|3x – 12| ≥ 6

3x – 12 ≥ 6 3x – 12 < -6

+12 +12 _ +12 +12

3x ≥ 18 3x < 6

3 3 3 3

x ≥ 6 x < 2

0 2 6