Answer:
see explanation
Step-by-step explanation:
The absolute value function always gives a positive result, however, the expression inside can be positive or negative.
The absolute value is a measure of the value from the origin and
| 2 | = | - 2 | = 2
Since 2 and - 2 are both 2 units from the origin.
Solving the given question
| 6 + y | = 2 , then
6 + y = 2 or - (6 + y) = 2
6 + y = 2 ( subtract 6 from both sides )
y = - 4
or
- (6 + y) = 2
- 6 - y = 2 ( add 6 to both sides )
- y = 8 ( multiply both sides by - 1 )
y = - 8
As a check
| 6 - 4 | = | 2 | = 2
| 6 - 8 | = | - 2 | = 2
Thus y = - 4 or y = - 8 are both solutions to the equation
