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Solving Absolute Value Equations

Learn how to solve absolute value equations with clear examples and detailed instructions. Master the process and techniques to find solutions easily.

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Solving Absolute Value Equations

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  1. Solving Absolute Value Equations • The absolute value ofx is defined as • Example 1

  2. Example 2

  3. Since and the solution is • Example 3 Solve: The process used above leads to our method for solving absolute value equations.

  4. To solve the absolute value equation 1) Write 2) Solve the resulting equations.

  5. Example 4 Solve: First, add 3 to both sides to get the equation in the form of

  6. Write the two equations and solve each.

  7. Example 5 Now solve the same problem again, only this time use the graphing method. Move all terms to the left hand side. Let y1 equal the left hand side.

  8. Enter the expression for y1 into the calculator Press Zoom-6 to graph Use Trace to find the x-intercepts

  9. Press Trace and then enter 3. Since the y-value is 0, (3,0) is an x-intercept, and 3 is a solution to the equation. Now repeat the process with x = 4, the intercept on the right. Again, the y-value is 0. The solutions to the equation are x = 3,4

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