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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Solving Absolute Value Equations

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Exercise 56 Page 34

For what numbers is the absolute value equal to 4?

always

Practice makes perfect

Let's consider the absolute value equation. |x-p|=4 We can think of p as a midpoint and 4 as a distance of the point x from that midpoint.

|x - Midpoint|= Distance to midpoint Any solution to the equation is a point x which is 4 units from the midpoint p. Since you can measure distance in both positive and negative directions on a number line, we will always have two solutions whose distance is 4 from the midpoint. Two examples are shown below.

We can write our conclusion.

For any real number p, the equation \|x-p\|=4 will always have two solutions.

Subchapter links

Communicate Your Answer p.27

Monitoring Progress p.28-31

Exercises p.32-34