ehwa23
Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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

 

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.