Answer :
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]
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]
