Answer :
Sure, let's solve the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] step-by-step.
First, we need to isolate the absolute value term:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
Subtract 6 from both sides:
[tex]\[ |x - 4| = 11 \][/tex]
The absolute value equation [tex]\( |x - 4| = 11 \)[/tex] means that the expression inside the absolute value can be either 11 or -11. So, we set up two separate equations to solve for [tex]\( x \)[/tex]:
1. [tex]\( x - 4 = 11 \)[/tex]
2. [tex]\( x - 4 = -11 \)[/tex]
### Solving the First Equation:
[tex]\[ x - 4 = 11 \][/tex]
Add 4 to both sides:
[tex]\[ x = 15 \][/tex]
### Solving the Second Equation:
[tex]\[ x - 4 = -11 \][/tex]
Add 4 to both sides:
[tex]\[ x = -7 \][/tex]
Therefore, the solutions to the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] are:
[tex]\[ x = 15 \quad \text{and} \quad x = -7 \][/tex]
So, the correct answer is:
[tex]\[ A. \, x = 15 \text{ and } x = -7 \][/tex]
First, we need to isolate the absolute value term:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
Subtract 6 from both sides:
[tex]\[ |x - 4| = 11 \][/tex]
The absolute value equation [tex]\( |x - 4| = 11 \)[/tex] means that the expression inside the absolute value can be either 11 or -11. So, we set up two separate equations to solve for [tex]\( x \)[/tex]:
1. [tex]\( x - 4 = 11 \)[/tex]
2. [tex]\( x - 4 = -11 \)[/tex]
### Solving the First Equation:
[tex]\[ x - 4 = 11 \][/tex]
Add 4 to both sides:
[tex]\[ x = 15 \][/tex]
### Solving the Second Equation:
[tex]\[ x - 4 = -11 \][/tex]
Add 4 to both sides:
[tex]\[ x = -7 \][/tex]
Therefore, the solutions to the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] are:
[tex]\[ x = 15 \quad \text{and} \quad x = -7 \][/tex]
So, the correct answer is:
[tex]\[ A. \, x = 15 \text{ and } x = -7 \][/tex]
