Answer:
|x+1|+|x−2|+−|x−2|=3+−|x−2|
|x+1|=−|x−2|+3
Either x+1=−|x−2|+3 or x+1=−(−|x−2|+3)
Part 1: x+1=−|x−2|+3
−|x−2|+3=x+1
−|x−2|+3+−3=x+1+−3(Add -3 to both sides)
−|x−2|=x−2
−|x−2| / −1 = x−2/ -1 (Divide both sides by -1)
|x−2|=−x+2
We know either x−2=−x+2 or x−2=−(−x+2)
x−2=−x+2(Possibility 1)
x−2+x=−x+2+x(Add x to both sides)
2x−2=2
2x−2+2=2+2(Add 2 to both sides)
2x=4
2x / 2 = 4/2
x=2
x−2=−(−x+2)(Possibility 2)
x−2=x−2(Simplify both sides of the equation)
x−2−x=x−2−x(Subtract x from both sides)
−2=−2
−2+2=−2+2(Add 2 to both sides)
0=0
Check answers. (Plug them in to make sure they work.)
x=2(Works in original equation)
0=0(Works in original equation)
Part 2: x+1=−(−|x−2|+3)
|x−2|−3=x+1
|x−2|−3+3=x+1+3(Add 3 to both sides)
|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
Check answers. (Plug them in to make sure they work.)
x=−1(Works in original equation)
Answer:
All real numbers are solutions.
I hope this is a great answers :)
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