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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 3 Page 210

How many cases do you have after you remove the absolute value?

Solutions: t=-3 and t=3
Graph:

Practice makes perfect

An absolute value measures an expression's distance from a midpoint on a number line. |2t|= 6 This equation means that the distance is 6, either in the positive direction or the negative direction. |2t|= 6 ⇒ l2t= 6 2t= -6 To find the solutions to the absolute value equation, we need to solve both of these cases for t.

| 2t|=6

lc 2t ≥ 0:2t = 6 & (I) 2t < 0:2t = - 6 & (II)

lc2t=6 & (I) 2t=-6 & (II)

(I), (II): .LHS /2.=.RHS /2.

lt=3 t=-3

Both 3 and -3 are solutions to the absolute value equation. Now, let's graph these solutions on a number line.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213

Exercise 3 Page 210

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