Absolute value equation |x-3|=5

8

Step-by-step explanation:

x-3=5

=x=5+3

x=8

x = - 2, x = 8

Step-by-step explanation:

The absolute value function always returns a positive value, but the expression inside can be positive or negative, thus

x - 3 = 5 OR - (x - 3) = 5

Solving both equations

x - 3 = 5 (add 3 to both sides)

x = 8

OR

- x + 3 = 5 (subtract 3 from both sides)

- x = 2 (multiply both sides by - 1)

x = - 2

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are solutions.

x = 8

| 8 - 3 | = | 5 | = 5 = right side

x = - 2

| - 2 - 3 | = | - 5 | = 5 = right side

Thus the solutions are x = - 2, x = 8