Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
2. Patterns and Linear Functions
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Exercise 23 Page 245

How many cases do we get when we remove the absolute value?

C

Practice makes perfect
An absolute value measures an expression's distance from a midpoint on a number line. |4x-11|= 13This equation means that the distance is 13, either in the positive direction or the negative direction. |4x-11|= 13 ⇒ l4x-11= 13 4x-11= - 13 To find the solutions to the absolute value equation, we need to solve both of these cases for x.
| 4x-11|=13

lc 4x-11 ≥ 0:4x-11 = 13 & (I) 4x-11 < 0:4x-11 = - 13 & (II)

lc4x-11=13 & (I) 4x-11=- 13 & (II)

(I), (II): LHS+11=RHS+11

lc4x=24 & (I) 4x=- 2 & (II)

(I), (II):.LHS /4.=.RHS /4.

lx_1=6 x_2=- 0.5
Both 6 and - 0.5 are solutions to the absolute value equation. This solution corresponds to the answer C.