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Pearson Algebra 1 Common Core, 2011 View details

4. Graphing a Function Rule

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Exercise 48 Page 259

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

-2,12

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An absolute value measures an expression's distance from a midpoint on a number line. |x-5|= 7This equation means that the distance is 7, either in the positive direction or the negative direction. |x-5|= 7 ⇒ lx-5= 7 x-5= - 7 To find the solutions to the absolute value equation, we need to solve both of these cases for x.

| x-5|=7

lc x-5 ≥ 0:x-5 = 7 & (I) x-5 < 0:x-5 = - 7 & (II)

lcx-5=7 & (I) x-5=- 7 & (II)

(I), (II): LHS+5=RHS+5

lx_1= 12 x_2=- 2

Both 12 and -2 are solutions to the absolute value equation.