Question

Explain this solution please...​

Answer 1

Let's solve your equation step-by-step.

|x|+|x−2|=2

Step 1: Add -|x-2| to both sides.

|x|+|x−2|+−|x−2|=2+−|x−2|

|x|=−|x−2|+2

Either x=−|x−2|+2 or x=−(−|x−2|+2)

Part 1: x=−|x−2|+2

(Flip the equation)

−|x−2|+2=x

−|x−2|+2+−2=x+−2(Add -2 to both sides)

−|x−2|=x−2

−|x−2|/1 = x-2/-1

(Divide both sides by -1)

|x−2|=−x+2

We know eitherx−2=−x+2orx−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

x=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=−(−|x−2|+2)

(Flip the equation)

|x−2|−2=x

|x−2|−2+2=x+2(Add 2 to both sides)

|x−2|=x+2

We know eitherx−2=x+2orx−2=−(x+2)

x−2=x+2(Possibility 1)

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

−2=2

−2+2=2+2(Add 2 to both sides)

0=4

x−2=−(x+2)(Possibility 2)

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

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=0

x= 0/2

x= 0

Hence , we conclude that :-

All real numbers are solutions.