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Pearson Algebra 1 Common Core, 2011 View details

7. Absolute Value Equations and Inequalities

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Exercise 52 Page 211

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

f=1 12 or f=-1 12

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

|f|-2/3=5/6

AddEqn

LHS+2/3=RHS+2/3

|f|-2/3+2/3=5/6+2/3

ExpandFrac

a/b=a * 2/b * 2

|f|-2/3+2/3=5/6+4/6

AddFrac

Add fractions

|f|=9/6

ReduceFrac

a/b=.a /3./.b /3.

|f|=3/2

FracToMixed

Write fraction as a mixed number

|f|=1 12

An absolute value measures an expression's distance from a midpoint on a number line. |f|= 1 12 This equation means that the distance is 1 12, either in the positive direction or the negative direction. |f|= 1 12 ⇒ lf= 1 12 f= -1 12 Both 1 12 and -1 12 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 52 Page 211

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