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**Do Now: Solve, graph, and write your answer in interval notation.**

CAUTION… you must THINK through your final answer!!! 1) a + 2 > -2 or a – 8 > 1 2) b – 3 > 2 and b + 3 < 4

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**Solving Absolute Value Inequalities**

Section: 1-6 Page 40 in your textbook

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**Solving an Absolute Value Inequality**

Step 1: Rewrite the inequality as a conjunction or a disjunction. If you have a you are working with a conjunction or an ‘and’ statement. Remember: “Less thand” If you have a you are working with a disjunction or an ‘or’ statement. Remember: “Greator” Step 2: In the second equation you must negate the right hand side and reverse the direction of the inequality sign. Step 3: Solve as a compound inequality.

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**Example 1: |2x + 1| > 7 2x + 1 > 7 or 2x + 1 >7**

This is an ‘or’ statement. (Greator). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. Write the solution in interval notation. |2x + 1| > 7 2x + 1 > 7 or 2x + 1 >7 2x + 1 >7 or 2x + 1 <-7 x > 3 or x < -4 (-inf., -4) U (3, +inf.) 3 -4

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**Example 2: |x -5|< 3 x -5< 3 and x -5< 3**

This is an ‘and’ statement. (Less thand). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. Write the solution in interval notation. |x -5|< 3 x -5< 3 and x -5< 3 x -5< 3 and x -5> -3 x < 8 and x > 2 (2, 8) 8 2

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**Example 3: |x |≥ -2 This is an ‘or’ statement. (Greator). Rewrite.**

x ≥ -2 or x ≤ 2 Solution: All Real Numbers ( -inf., +inf.) This is an ‘or’ statement. (Greator). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. Write the solution in interval notation.

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**Example 4: |2x| < -4 2x < -4 and 2x > 4**

NO SOLUTION!! This is an ‘and’ statement. (Less thand). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. Write the solution in interval notation.

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**1) |y – 3| > 1 2) |p + 2| < 6 3) | g | - 2 < -4**

Solve and Graph 1) |y – 3| > 1 2) |p + 2| < 6 3) | g | - 2 < -4

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Solving Absolute Value Inequalities. Solving Absolute Value Inequalities 1. ax+b 0 Becomes an “and” problem Changes to: –c < ax+b < c 2. ax+b > c, where.

Solving Absolute Value Inequalities. Solving Absolute Value Inequalities 1. ax+b 0 Becomes an “and” problem Changes to: –c < ax+b < c 2. ax+b > c, where.

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