Solve the equations. Check your solutions. |x-2|=|4+x|

x = -1

Step-by-step explanation:

Solve Absolute Value.

|x−2|=|x+4|

We know eitherx−2=x+4orx−2=−(x+4)

x−2=x+4(Possibility 1)

x−2−x=x+4−x(Subtract x from both sides)

−2=4

−2+2=4+2(Add 2 to both sides)

0=6

x−2=−(x+4)(Possibility 2)

x−2=−x−4(Simplify both sides of the equation)

x−2+x=−x−4+x(Add x to both sides)

2x−2=−4

2x−2+2=−4+2(Add 2 to both sides)

2x=−2

2x

2

=

−2

2

(Divide both sides by 2)

x=−1

Hope this helps!

-Josh

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step-by-step explanation:

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