Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Solve [tex]|x-4|+6=17[/tex]

A. [tex]x=15[/tex] and [tex]x=-7[/tex]

B. [tex]x=15[/tex] and [tex]x=-15[/tex]

C. [tex]x=-15[/tex] and [tex]x=7[/tex]

D. [tex]x=-15[/tex] and [tex]x=-7[/tex]

Sure, let's solve the given equation step by step:

The given equation is:
[tex]\[ |x - 4| + 6 = 17 \][/tex]

Step 1: Isolate the absolute value term.

To do that, we subtract 6 from both sides of the equation:
[tex]\[ |x - 4| + 6 - 6 = 17 - 6 \][/tex]
[tex]\[ |x - 4| = 11 \][/tex]

Step 2: Solve the absolute value equation.

An absolute value equation [tex]\( |A| = B \)[/tex] has two possible solutions:
1. [tex]\( A = B \)[/tex]
2. [tex]\( A = -B \)[/tex]

In our case, [tex]\( A = x - 4 \)[/tex] and [tex]\( B = 11 \)[/tex].

So, we have two equations to solve:
1. [tex]\( x - 4 = 11 \)[/tex]
2. [tex]\( x - 4 = -11 \)[/tex]

Step 3: Solve each equation separately.

For the first equation:
[tex]\[ x - 4 = 11 \][/tex]
Add 4 to both sides:
[tex]\[ x = 11 + 4 \][/tex]
[tex]\[ x = 15 \][/tex]

For the second equation:
[tex]\[ x - 4 = -11 \][/tex]
Add 4 to both sides:
[tex]\[ x = -11 + 4 \][/tex]
[tex]\[ x = -7 \][/tex]

Step 4: Write the final solutions.

The solutions to the given equation [tex]\( |x - 4| + 6 = 17 \)[/tex] are:
[tex]\[ x = 15 \text{ and } x = -7 \][/tex]

Therefore, the correct answer is:
A. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex]