Question

Below are the steps to solve an equation:

Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4

Which of the following is a correct next step to solve the equation?
x + 2 = −4
−x − 2 = 4
x + 2 = 4
x − 2 = −4

I thought it was B, but I got it wrong. Could some one please help me?

Answer 1

If I said that \(|x-y|\)=z, what are the two posibilities?

Answer 2

|x − 2| = 4
Remove absolute
x-2=-4

Answer 3

@Lyralei, there is more than 1 posibility for that

Answer 4

hears all the steps
Let's solve your equation step-by-step.
|x−2|+3=7
Step 1: Add -3 to both sides.
|x−2|+3+−3=7+−3
|x−2|=4
Step 2: Solve Absolute Value.
|x−2|=4
We know either x−2=4 or x−2=−4
x−2=4(Possibility 1)
x−2+2=4+2(Add 2 to both sides)
x=6
x−2=−4(Possibility 2)
x−2+2=−4+2(Add 2 to both sides)
x=−2
Answer:
x=6 or x=−2

Answer 5

Okay, well that dosent work. Because I already know that x=-2
@Ahsome

Answer 6

like @Ahsome said |x+y| = z have two answers
x+y =z or x+y =-z

Answer 7

Yes @Anastashia. What are the two posibilities?