Solve the absolute value equation.
|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
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.