Question

Solve the equation with the replacement set {–34, –2, 2, 34}

|16 – x| = 18



–2, 2

–2, 34


2

–34

Answer 1

Solve for x over the integers:
abs(16 - x) = 18
Split the equation into two possible cases:
16 - x = 18 or 16 - x = -18
Subtract 16 from both sides:
-x = 2 or 16 - x = -18
Multiply both sides by -1:
x = -2 or 16 - x = -18
Subtract 16 from both sides:
x = -2 or -x = -34
Multiply both sides by -1:
Answer: x = -2 or x = 34

Answer 2

Option 2 - The required solution is -2 and 34.

Explanation:

Given : Equation,
`|16-x|=18`

To find : Solve the equation with the replacement set {–34, –2, 2, 34} ?

Solution :

The equation
`|16-x|=18` is written as,

`16-x=18` and
`16-x=-18`

Substitute the values from set if it satisfy the equation that is the solution,

1) Put x=-34,

`16-(-34)=16+34=50\\eq 18`

Not true.

2) Put x=-2,

`16-x=16-(-2)=16+2=18`

True.

3) Put x=2,

`16-x=16-(2)=14\\eq 18`

Not true.

4) Put x=34

`16-x=16-(34)=-18`

True.

Therefore, The required solution is -2 and 34.

So, Option 2 is correct.