Question

Solve the absolute value equation. 4 − |x| = 1

Answer 1

Answer: 3 and -3

Step-by-step explanation:

Here's why: normally if this were a normal equation the answer would be -3. But the absolute value sign changes something making it 3 because of the absolute value and -3 because of the original equation answer without the absolute value symbol.

Answer 2

Answer:

x = +3 and -3

Step-by-step explanation:

Start by solving for |x| as normal:

4 - |x| = 1

- |x| = -3 (subtract 4 from both sides)

|x| = 3 (multiply both sides by -1)

the absolute value of x means it will be positive, so you need to recognize that whatever is in the absolute value bars will be made positive.

this means that x = 3 AND -3, because both |3| and |-3| = 3

check your answer by plugging x = 3 and x = -3 back in:

4 - |3| = 1

4 - 3 = 1

1 = 1

and

4 - |-3| = 1

4 - 3 =  1

1 = 1