Solve the absolute value equation.

Question

|x-2|+4=7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
А.
The solution set is ___
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
• В.
The solution set no solution

Answer 1

To solve the equation |x-2|+4=7, we will first subtract 4 from both sides to isolate the absolute value term:

|x-2| = 3

We can then split the equation into two separate cases, one for when the expression inside the absolute value is positive and one for when it is negative.

Case 1: x-2 is positive
If x-2 is positive, then |x-2| = (x-2). Substituting into the equation, we have:

(x-2) = 3
x - 2 = 3
x = 5

Case 2: x-2 is negative
If x-2 is negative, then |x-2| = -(x-2). Substituting into the equation, we have:

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

So the solution set is x = 5, -1.

Therefore, the correct choice is А. The solution set is 5, -1.