Question

Solve the following absolute value equation.

\2+5) = 8
x = 51
X = - [?]
Notice that the negative sign is already entered!
Enter​

Answer 1

x = - 61

Explanation:

The absolute function always returns a positive value.

However, the expression inside can be positive or negative.

Given

`(|x+5|)/(7)` = 8 ( multiply both sides by 7 )

| x + 5 | = 56, thus

x + 5 = 56 OR - (x + 5) = 56

Solve

x + 5 = 56 ( subtract 5 from both sides )

x = 51 ← given solution

OR

- (x + 5) = 56 ← distribute left side

- x - 5 = 56 ( add 5 to both sides )

- x = 61 ( multiply both sides by - 1 )

x = - 61 ← required solution