# 1.6 – Solving Compound and Absolute Value Inequalities

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

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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
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
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 > or y + 4 ≤ -3

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

Example 2 – Solve y – 2 > -3 or y + 4 ≤ -3 and
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 > or y + 4 ≤ -3 y > or y ≤ -7 -7 -1

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

(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 -4 4

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

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

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

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

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

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

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

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

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

Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ x – 12 < -6 _ 3x ≥ x < 6 x ≥ x < 2

Example 4 – Solve |3x – 12| ≥ 6 and graph the
Example 4 – Solve |3x – 12| ≥ 6 and graph the solution on a number line. |3x – 12| ≥ 6 3x – 12 ≥ x – 12 < -6 _ 3x ≥ x < 6 x ≥ x < 2 2 6