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Solving an Absolute Value Equation

Solving an Absolute Value Equation. Solve an absolute value equation (with an equal sign) Solve and absolute value inequality. Solving an Absolute Value Equation. Solve |a – 4| = 3. Case 1: write the problem as you see it without the absolute value signs and solve: a – 4 = 3

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Solving an Absolute Value Equation

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  1. Solving an Absolute Value Equation • Solve an absolute value equation (with an equal sign) • Solve and absolute value inequality

  2. Solving an Absolute Value Equation Solve |a – 4| = 3 Case 1: write the problem as you see it without the absolute value signs and solve: a – 4 = 3 a = 7 Case 2: write it as you see it but change the sign of the “answer” and then solve: a – 4 = -3 a = 1 OR

  3. Now you try:Solve |x + 6| = 8 x + 6 = 8 x = 2 x + 6 = -8 x = -14 OR Question? Can an absolute value ever equal a negative number? ??? |x + 6| = -2 ??? NO solution!

  4. Same steps as before with one extra step in Step 2: solve |n + 3| < 5 Solving Absolute Value with an Inequality Case 1: write the problem as you see it without the absolute value signs and solve: n + 3 < 5 n < 2 Case 2: write it as you see it but change the inequality AND the sign of the “answer” and then solve: n + 3 > -5 n > -8 and

  5. Summary of Absolute Value Problems If |x| = n, then x = n OR x = -n If |x| < n, then x < n AND x > -n If |x| > n, then x > n OR x < -n -n n -5 5

  6. If given a graph and you have to write the equation: Step 1: write the “skeleton” equation |x +c | ab

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