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Pearson Algebra 1 Common Core, 2011 View details

4. Graphing a Function Rule

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Exercise 50 Page 259

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

1,13

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An absolute value measures an expression's distance from a midpoint on a number line. 6=|a-7| ⇔ |a-7|= 6This equation means that the distance is 6, either in the positive direction or the negative direction. |a-7|= 6 ⇒ la-7= 6 a-7= -6 To find the solutions to the absolute value equation, we need to solve both of these cases for a.

|a-7|=6

lc a-7 ≥ 0:a-7 = 6 & (I) a-7 < 0:a-7 = - 6 & (II)

lca-7= 6 & (I) a-7=-6 & (II)

(I), (II): LHS+7=RHS+7

la_1=13 a_2=1

Both 13 and 1 are solutions to the absolute value equation.