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Solve the equation:
| x + 1 | + |x - 2 | = 3

Sagot :

miriammenenguez

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 :)

Happy friday

 

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