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

Answer:x = 8Step-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) < 0Then 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 ≥ -2x+2-3 = 0.5x+1Subtracting 0.5x both sides:x - 0.5x -3 = 0.5x - 0.5x +10.5x -3 = 1Adding 3 both sides:0.5x -3 +3 = 1 +30.5x = 4Dividing by 0.5x = 4/0.5x = 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 +1Applying the distributive property:-x+2-3=0.5x+1-x-1=0.5x+1Adding 1 both sides:-x =0.5x +2Subtracting 0.5x both sides:-x-0.5x = 2-1.5x =2Dividing by -1.5x = - 4/3. But x > -2 therefore is not a solution.