Solve for x in the following equation: |x + 2| - 3 = 0.5x + 1.

x = 8

Step-by-step explanation:

In order to solve the equation, you have to apply the definition of absolute value function, which is:

|f (x) | = f (x) if f (x) ≥ 0

|f (x) | = - f (x) if f (x) < 0

Then you have to solve the equation for both cases.

In this case, f (x) = x+2

-For x+2 ≥ 0 which is equivalent to x ≥ - 2

x+2-3 = 0.5x+1

Subtracting 0.5x both sides:

x - 0.5x - 3 = 0.5x - 0.5x + 1

0.5x - 3 = 1

Adding 3 both sides:

0.5x - 3 + 3 = 1 + 3

0.5x = 4

Dividing by 0.5

x = 4/0.5

x = 8. This is a solution because x ≥ - 2

- For x+2<0 which is equivalent to x < - 2 then |x + 2| = - (x+2)

- (x-2) - 3 = 0.5x + 1

Applying the distributive property:

-x+2-3=0.5x+1

-x-1=0.5x+1

Adding 1 both sides:

-x = 0.5x + 2

Subtracting 0.5x both sides:

-x-0.5x = 2

-1.5x = 2

Dividing by - 1.5

x = - 4/3. But x > - 2 therefore is not a solution.