Let's solve the equation [tex]\( 100 - \frac{1}{2} x = 92 \)[/tex] step by step to determine the number of questions [tex]\( x \)[/tex] that Jen answered incorrectly.
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[ 100 - \frac{1}{2} x = 92 \][/tex]
2. Subtract 100 from both sides:
[tex]\[ 100 - \frac{1}{2} x - 100 = 92 - 100 \][/tex]
Simplifying this, we get:
[tex]\[ -\frac{1}{2} x = -8 \][/tex]
3. Multiply both sides by -2 to isolate [tex]\( x \)[/tex]:
[tex]\[ -2 \left( -\frac{1}{2} x \right) = -2 \left( -8 \right) \][/tex]
Simplifying this, we get:
[tex]\[ x = 16 \][/tex]
So, the value of [tex]\( x \)[/tex] is 16.
### Analysis of Jen's Steps:
Jen's steps were as follows:
1. She subtracted 100 from both sides, which is the correct first step:
[tex]\[ 100 - \frac{1}{2} x = 92 \][/tex]
[tex]\[ -\frac{1}{2} x = -8 \][/tex]
2. She then multiplied both sides by -2, which is also correct:
[tex]\[ x = 16 \][/tex]
Based on the provided options, the correct one should match the above steps. The accurate option is:
- Correct. She could have also subtracted 100 from both sides, then divided by [tex]\(-\frac{1}{2}\)[/tex].
Indeed, after subtracting 100 from both sides to get:
[tex]\[ -\frac{1}{2} x = -8 \][/tex]
she could have alternatively divided both sides by [tex]\(-\frac{1}{2}\)[/tex] instead of multiplying by -2. Dividing both sides by [tex]\(-\frac{1}{2}\)[/tex] would also isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-8}{-\frac{1}{2}} = 16 \][/tex]
Thus, the most accurate description of Jen's work is:
Correct. She could have also subtracted 100 from both sides, then divided by [tex]\( -\frac{1}{2} \)[/tex].
