Math

QuestionSolve the equation: x+132=20\frac{|x+13|}{-2}=-20.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is always non-negative. . The equation is x+13=20\frac{|x+13|}{-}=-20.

STEP 2

We first multiply both sides of the equation by -2 to get rid of the denominator.
2×x+132=2×20-2 \times \frac{|x+13|}{-2} = -2 \times -20

STEP 3

After multiplying, we getx+13=40|x+13| =40

STEP 4

The absolute value of a number is the distance of that number from zero on the number line, and it is always non-negative. Therefore, if x+13=40|x+13| =40, then x+13x+13 can be either40 or -40.
So, we have two equations to solve1. x+13=40x+13 =40
2. x+13=40x+13 = -40

STEP 5

olving the first equation x+13=40x+13 =40 for xxx=4013x =40 -13

STEP 6

Calculate the value of xx from the first equationx=4013=27x =40 -13 =27

STEP 7

olving the second equation x+13=40x+13 = -40 for xxx=4013x = -40 -13

STEP 8

Calculate the value of xx from the second equationx=4013=53x = -40 -13 = -53So, the solutions to the equation x+132=20\frac{|x+13|}{-2}=-20 are x=27x =27 and x=53x = -53.

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