Answer:
x = 8
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.