Math

QuestionSolve for xx: 2x+25=10\frac{-|2 x+2|}{5}=-10

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is always non-negative.. The absolute value of a number is the distance of the number from zero on the number line, regardless of the direction.
3. The equation is x+5=10\frac{-| x+|}{5}=-10.

STEP 2

First, we need to isolate the absolute value. We can do this by multiplying both sides of the equation by -5.
5×2x+25=5×10-5 \times \frac{-|2 x+2|}{5} = -5 \times -10

STEP 3

implify the equation.
2x+2=50|2 x+2| =50

STEP 4

The absolute value of a number can be either positive or negative. Therefore, we can write two equations from the absolute value equation.
2x+2=502 x+2 =502x+2=502 x+2 = -50

STEP 5

olve the first equation for x.
2x=5022 x =50 -22x=482 x =48x=482x = \frac{48}{2}x=24x =24

STEP 6

olve the second equation for x.
2x=5022 x = -50 -22x=522 x = -52x=522x = \frac{-52}{2}x=26x = -26The solutions to the equation 2x+25=10\frac{-|2 x+2|}{5}=-10 are x=24x =24 and x=26x = -26.

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