Answer :
We start with the equation:
[tex]$$
4|x-3| + 2 = 18.
$$[/tex]
Step 1. Subtract [tex]$2$[/tex] from both sides to isolate the absolute value term:
[tex]$$
4|x-3| = 18 - 2 = 16.
$$[/tex]
Step 2. Divide both sides by [tex]$4$[/tex] to solve for the absolute value:
[tex]$$
|x-3| = \frac{16}{4} = 4.
$$[/tex]
Step 3. The equation [tex]$|x-3| = 4$[/tex] means that the expression inside the absolute value can be either [tex]$4$[/tex] or [tex]$-4$[/tex]. This gives us two cases:
1. If [tex]$x - 3 = 4$[/tex], then
[tex]$$
x = 4 + 3 = 7.
$$[/tex]
2. If [tex]$x - 3 = -4$[/tex], then
[tex]$$
x = -4 + 3 = -1.
$$[/tex]
Thus, the solutions are [tex]$x = 7$[/tex] and [tex]$x = -1$[/tex]. This corresponds to option B:
[tex]$$
x = -1 \quad \text{and} \quad x = 7.
$$[/tex]
[tex]$$
4|x-3| + 2 = 18.
$$[/tex]
Step 1. Subtract [tex]$2$[/tex] from both sides to isolate the absolute value term:
[tex]$$
4|x-3| = 18 - 2 = 16.
$$[/tex]
Step 2. Divide both sides by [tex]$4$[/tex] to solve for the absolute value:
[tex]$$
|x-3| = \frac{16}{4} = 4.
$$[/tex]
Step 3. The equation [tex]$|x-3| = 4$[/tex] means that the expression inside the absolute value can be either [tex]$4$[/tex] or [tex]$-4$[/tex]. This gives us two cases:
1. If [tex]$x - 3 = 4$[/tex], then
[tex]$$
x = 4 + 3 = 7.
$$[/tex]
2. If [tex]$x - 3 = -4$[/tex], then
[tex]$$
x = -4 + 3 = -1.
$$[/tex]
Thus, the solutions are [tex]$x = 7$[/tex] and [tex]$x = -1$[/tex]. This corresponds to option B:
[tex]$$
x = -1 \quad \text{and} \quad x = 7.
$$[/tex]