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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 24 Page 211

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

d=0 or d=-8

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

2|d+4|=8

DivEqn

.LHS /2.=.RHS /2.

|d+4|=4

An absolute value measures an expression's distance from a midpoint on a number line.

|d+4|= 4 This equation means that the distance is 4, either in the positive direction or the negative direction. |d+4|= 4 ⇒ ld+4= 4 d+4= -4 To find the solutions to the absolute value equation, we need to solve both of these cases for d.

| d+4|=4

lc d+4 ≥ 0:d+4 = 4 & (I) d+4 < 0:d+4 = - 4 & (II)

lcd+4=4 & (I) d+4=-4 & (II)

(I), (II): LHS-4=RHS-4

ld_1=0 d_2=-8

Both d=0 and d=-8 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

Exercise 24 Page 211

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