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1.6 – Solving Compound and Absolute Value Inequalities

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

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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

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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

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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

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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

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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

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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

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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

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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

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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 6

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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 6 <

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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 6 < 2x

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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 6 < 2x 2 2

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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 6 < 2x 2 2 3

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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 6 < 2x 2 2 3 <

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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 6 < 2x 2 2 3 < x

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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

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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 2x 2 2 3 < x

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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 2x < 2 2 3 < x

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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 2x < 10 2 2 3 < x

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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 2x ≤ 10 2 2 2 2 3 < x

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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 2x ≤ 10 2 2 2 2 3 < x x

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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 2x ≤ 10 2 2 2 2 3 < x x <

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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 2x ≤ 10 2 2 2 2 3 < x x < 5

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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 2x ≤ 10 2 2 2 2 3 < x x < 5

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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 2x ≤ 10 2 2 2 2 3 < x x < 5 3 < x

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x < 5

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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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 2x ≤ 10 2 2 2 2 3 < x x ≤ 5 3 < x ≤ 5 0 35

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

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y – 2 > -3 or y + 4 ≤ -3

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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

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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 +2 +2 -4 -4

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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 +2 +2 -4 -4 y > -1 or y ≤ -7

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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 +2 +2 -4 -4 y > -1 or y ≤ -7

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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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 +2 +2 -4 -4 y > -1 or y ≤ -7 -7 0

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line.

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 -4 04

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. -4 04

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 -4 04

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 a > 4 or a < -4 -4 04

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Example 3 (a) Solve |a| < 4. Graph the solution on a number line. |a| < 4 a -4 (b) Solve |a| > 4. Graph the solution on a number line. |a| > 4 a > 4 or a < -4 -4 04 04

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

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|3x – 12| ≥ 6

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

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

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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

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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

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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

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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

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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 26

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