To solve the given absolute value equation, follow these steps:
Given:
[tex]\[ \frac{|x + 6|}{7} = 2 \][/tex]
1. Isolate the absolute value expression:
Multiply both sides of the equation by 7:
[tex]\[ |x + 6| = 2 \times 7 \][/tex]
[tex]\[ |x + 6| = 14 \][/tex]
2. Set up two cases for the absolute value equation:
The absolute value equation [tex]\(|x + 6| = 14\)[/tex] can be split into two separate equations:
- Case 1: [tex]\[ x + 6 = 14 \][/tex]
- Case 2: [tex]\[ x + 6 = -14 \][/tex]
3. Solve Case 1:
[tex]\[ x + 6 = 14 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 14 - 6 \][/tex]
[tex]\[ x = 8 \][/tex]
4. Solve Case 2:
[tex]\[ x + 6 = -14 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -14 - 6 \][/tex]
[tex]\[ x = -20 \][/tex]
So the solutions to the equation [tex]\(\frac{|x + 6|}{7} = 2\)[/tex] are:
1. [tex]\( x = 8 \)[/tex]
2. [tex]\( x = -20 \)[/tex]
Given the format of the question:
[tex]\[ x = 8 \][/tex]
[tex]\[ x = -[\text{?}] \][/tex]
We see that the second solution is [tex]\( x = -20 \)[/tex].
Therefore, the correct value for the unknown number is:
[tex]\[ x = -20 \][/tex]
