Sure, I'd be happy to help you solve the given equation step-by-step.
The equation given is:
[tex]\[ 2|x-6| + 14 = 38 \][/tex]
Let's solve for [tex]\( x \)[/tex] by isolating the absolute value expression. Here are the steps:
1. Subtract 14 from both sides of the equation:
[tex]\[ 2|x-6| + 14 - 14 = 38 - 14 \][/tex]
[tex]\[ 2|x-6| = 24 \][/tex]
2. Divide both sides by 2:
[tex]\[ \frac{2|x-6|}{2} = \frac{24}{2} \][/tex]
[tex]\[ |x-6| = 12 \][/tex]
3. Remove the absolute value by considering the two possible cases:
- [tex]\( x-6 = 12 \)[/tex]
- [tex]\( x-6 = -12 \)[/tex]
Solving these two separate equations:
- For the first case [tex]\( x-6 = 12 \)[/tex]:
[tex]\[ x - 6 = 12 \][/tex]
[tex]\[ x = 12 + 6 \][/tex]
[tex]\[ x = 18 \][/tex]
- For the second case [tex]\( x-6 = -12 \)[/tex]:
[tex]\[ x - 6 = -12 \][/tex]
[tex]\[ x = -12 + 6 \][/tex]
[tex]\[ x = -6 \][/tex]
4. Thus, the possible solutions are:
[tex]\[ x = 18 \quad \text{and} \quad x = -6 \][/tex]
Given the possible values of [tex]\( x \)[/tex], the minimum temperature is [tex]\( -6 \)[/tex] and the maximum temperature is [tex]\( 18 \)[/tex].
Therefore, the minimum and maximum temperatures for this day are:
[tex]\[ \boxed{x = -6 \text{ and } x = 18} \][/tex]
So the correct choice from the options provided is:
[tex]\[ x = -6, x = 18 \][/tex]
