Answer :
We start with the equation
[tex]$$
|x-5| + 7 = 17.
$$[/tex]
Step 1. Isolate the absolute value by subtracting 7 from both sides:
[tex]$$
|x-5| = 17 - 7 = 10.
$$[/tex]
Step 2. Now, the equation
[tex]$$
|x-5| = 10
$$[/tex]
means that the expression inside the absolute value can be either 10 or [tex]$-10$[/tex]. This gives us two cases:
Case 1:
[tex]$$
x - 5 = 10.
$$[/tex]
Add 5 to both sides:
[tex]$$
x = 10 + 5 = 15.
$$[/tex]
Case 2:
[tex]$$
x - 5 = -10.
$$[/tex]
Add 5 to both sides:
[tex]$$
x = -10 + 5 = -5.
$$[/tex]
Thus, the solutions are [tex]$x = 15$[/tex] and [tex]$x = -5$[/tex]. Comparing with the answer options, the correct choice is:
D. [tex]$x=15$[/tex] and [tex]$x=-5$[/tex].
[tex]$$
|x-5| + 7 = 17.
$$[/tex]
Step 1. Isolate the absolute value by subtracting 7 from both sides:
[tex]$$
|x-5| = 17 - 7 = 10.
$$[/tex]
Step 2. Now, the equation
[tex]$$
|x-5| = 10
$$[/tex]
means that the expression inside the absolute value can be either 10 or [tex]$-10$[/tex]. This gives us two cases:
Case 1:
[tex]$$
x - 5 = 10.
$$[/tex]
Add 5 to both sides:
[tex]$$
x = 10 + 5 = 15.
$$[/tex]
Case 2:
[tex]$$
x - 5 = -10.
$$[/tex]
Add 5 to both sides:
[tex]$$
x = -10 + 5 = -5.
$$[/tex]
Thus, the solutions are [tex]$x = 15$[/tex] and [tex]$x = -5$[/tex]. Comparing with the answer options, the correct choice is:
D. [tex]$x=15$[/tex] and [tex]$x=-5$[/tex].
