|x+1|+|xβ2|+β|xβ2|=3+β|xβ2|
|x+1|=β|xβ2|+3
Either x+1=β|xβ2|+3 or x+1=β(β|xβ2|+3)
Part 1: x+1=β|xβ2|+3
β|xβ2|+3=x+1
β|xβ2|+3+β3=x+1+β3(Add -3 to both sides)
β|xβ2|=xβ2
β|xβ2| / β1 Β = xβ2/ -1 (Divide both sides by -1)
|xβ2|=βx+2
We know either xβ2=βx+2 or xβ2=β(βx+2)
xβ2=βx+2(Possibility 1)
xβ2+x=βx+2+x(Add x to both sides)
2xβ2=2
2xβ2+2=2+2(Add 2 to both sides)
2x=4
2x / 2 = 4/2
x=2
xβ2=β(βx+2)(Possibility 2)
xβ2=xβ2(Simplify both sides of the equation)
xβ2βx=xβ2βx(Subtract x from both sides)
β2=β2
β2+2=β2+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=β(β|xβ2|+3)
|xβ2|β3=x+1
|xβ2|β3+3=x+1+3(Add 3 to both sides)
|xβ2|=x+4
We know eitherxβ2=x+4orxβ2=β(x+4)
xβ2=x+4(Possibility 1)
xβ2βx=x+4βx(Subtract x from both sides)
β2=4
β2+2=4+2(Add 2 to both sides)
0=6
xβ2=β(x+4)(Possibility 2)
xβ2=βxβ4(Simplify both sides of the equation)
xβ2+x=βxβ4+x(Add x to both sides)
2xβ2=β4
2xβ2+2=β4+2(Add 2 to both sides)
2x=β2
2x/2 = -2/2 Β (Divide both sides by 2)
x=β1
Check answers. (Plug them in to make sure they work.)
x=β1(Works in original equation)
All real numbers are solutions.
I hope this is a great answers :)
Happy friday
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