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Solving Absolute Value Equations & Inequalities

Learn how to solve absolute value equations and inequalities by understanding the concept of distance from zero. This slideshow covers various examples and solutions.

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Solving Absolute Value Equations & Inequalities

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  1. Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

  2. More Equations and Inequalities Section 9.1

  3. 9 More Equations and Inequalities 9.1 Solving Absolute Value Equations 9.2 Solving Absolute Value Inequalities 9.3 Solving Linear and Compound Linear Inequalities in Two Variables 9.4 Solving Systems of Linear Equations Using Matrices

  4. 9.1 Solving Absolute Value Equations The “distance from zero” is the Absolute Value. The absolute value of a number is the distance between that number and 0 on the number line. It just describes the distance, not what side of zero the number is on. The absolute value of a number is always positive or zero. Distance = 4 Distance = 4 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 We use this idea of distance from zero to solve absolute value equations and inequalities.

  5. Understand the Meaning of an Absolute Value Equation Example 1 Solution Since the equation contains an absolute value, we need to find the number or numbers whose distance from zero is 4. Distance = 4 Distance = 4 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Notice that 4 and -4 are 4 units from zero. Therefore the solution set is {-4,4}. Check. and

  6. Example 2 Solution To find the number that can be substituted for n we let n+3=7 and n+3=-7 since both 7 and -7 are 7 units from zero. Set the quantity inside the absolute value equal to 7 and -7. Solve each equation for n. The solution set is {-10, 4}.

  7. In the previous slide, n = 4 and n=-10. Let’s check our answer by substituting our solutions into original equation. Check: Check: |4+3|=7 |-10+3|=7 |7|=7 |-7|=7 The solution set is {-10, 4}.

  8. Example 3 Solution First isolate the absolute value. That is get the absolute value on a side by itself. Subtract 3 from both sides. Set the quantity inside the absolute value equal to 2 and -2. Add 2 on both sides. Multiply by 4 on both sides. The solution set is {0, 16}.

  9. Solution The quantities are negatives of each other. The quantities are the same.

  10. Example 4 Solution This equation says that the absolute value of the quantity equals negative 8. Can an absolute value be negative? NO! This equation has no solution because the absolute value will never be negative.

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