Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
5. Rewriting Equations and Formulas
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Exercise 52 Page 42

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

Solutions: y=7 and y=1
Number Line:

Practice makes perfect
Before we can solve this equation, we need to isolate the absolute value expression using the Properties of Equality.
|3y-12|-7=2
|3y-12|=9
An absolute value measures an expression's distance from a midpoint on a number line. |3y-12|= 9 This equation means that the distance is 9, either in the positive direction or the negative direction. |3y-12|= 9 ⇒ l3y-12= 9 3y-12= - 9 To find the solutions to the absolute value equation, we need to solve both of these cases for y.
| 3y-12|=9

lc 3y-12 ≥ 0:3y-12 = 9 & (I) 3y-12 < 0:3y-12 = - 9 & (II)

lc3y-12=9 & (I) 3y-12=-9 & (II)

(I), (II): LHS+12=RHS+12

l3y=21 3y=3

(I), (II): .LHS /3.=.RHS /3.

ly=7 y=1
Both y=7 and y=1 are solutions to the absolute value equation. Let's graph these solutions on a number line.