Answer :
Sure, let me show you how to solve this step-by-step:
We start with the given equation:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
1. Isolate the absolute value expression
- Subtract 6 from both sides of the equation:
[tex]\[ |x - 4| = 17 - 6 \][/tex]
[tex]\[ |x - 4| = 11 \][/tex]
2. Solve the absolute value equation
- The basic property of absolute values is that if [tex]\(|A| = B\)[/tex], then [tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex]. We can apply this property here:
[tex]\[ x - 4 = 11 \quad \text{or} \quad x - 4 = -11 \][/tex]
3. Solve each case separately
- For the first case:
[tex]\[ x - 4 = 11 \][/tex]
- Add 4 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 11 + 4 \][/tex]
[tex]\[ x = 15 \][/tex]
- For the second case:
[tex]\[ x - 4 = -11 \][/tex]
- Add 4 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = -11 + 4 \][/tex]
[tex]\[ x = -7 \][/tex]
4. Summarize the solutions:
[tex]\[ x = 15 \quad \text{and} \quad x = -7 \][/tex]
So, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] are [tex]\( 15 \)[/tex] and [tex]\( -7 \)[/tex].
The correct answer is C. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
We start with the given equation:
[tex]\[ |x - 4| + 6 = 17 \][/tex]
1. Isolate the absolute value expression
- Subtract 6 from both sides of the equation:
[tex]\[ |x - 4| = 17 - 6 \][/tex]
[tex]\[ |x - 4| = 11 \][/tex]
2. Solve the absolute value equation
- The basic property of absolute values is that if [tex]\(|A| = B\)[/tex], then [tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex]. We can apply this property here:
[tex]\[ x - 4 = 11 \quad \text{or} \quad x - 4 = -11 \][/tex]
3. Solve each case separately
- For the first case:
[tex]\[ x - 4 = 11 \][/tex]
- Add 4 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 11 + 4 \][/tex]
[tex]\[ x = 15 \][/tex]
- For the second case:
[tex]\[ x - 4 = -11 \][/tex]
- Add 4 to both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = -11 + 4 \][/tex]
[tex]\[ x = -7 \][/tex]
4. Summarize the solutions:
[tex]\[ x = 15 \quad \text{and} \quad x = -7 \][/tex]
So, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( |x - 4| + 6 = 17 \)[/tex] are [tex]\( 15 \)[/tex] and [tex]\( -7 \)[/tex].
The correct answer is C. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
