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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 22 Page 211

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

w=2 or w=-2

Practice makes perfect

Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.

-3|2w|=-12

.LHS /(-3).=.RHS /(-3).

|2w|=4

An absolute value measures an expression's distance from a midpoint on a number line. |2w|= 4 This equation means that the distance is 4, either in the positive direction or the negative direction. |2w|= 4 ⇒ l2w= 4 2w= -4 To find the solutions to the absolute value equation, we need to solve both of these cases for w.

| 2w|=4

lc 2w ≥ 0:2w = 4 & (I) 2w < 0:2w = - 4 & (II)

lc2w=4 & (I) 2w=-4 & (II)

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

lw_1=2 w_2=-2

Both w=2 and w=-2 are solutions to the absolute value equation.

Subchapter links

Lesson Check p.210

Practice and Problem-Solving Exercises p.211-213

Standardized Test Prep p.213

Mixed Review p.213