Let's carefully analyze the steps that Jen took to solve the equation [tex]\(100 - \frac{1}{2}x = 92\)[/tex].
### Step-by-step analysis:
1. Initial Equation:
[tex]\[
100 - \frac{1}{2}x = 92
\][/tex]
2. Jen's first step: Subtract 100 from both sides
[tex]\[
100 - \frac{1}{2}x - 100 = 92 - 100
\][/tex]
Simplifies to:
[tex]\[
-\frac{1}{2}x = -8
\][/tex]
3. Jen's second step: Multiply both sides by -2
[tex]\[
-2 \cdot \left(-\frac{1}{2}x\right) = -2 \cdot (-8)
\][/tex]
Simplifies to:
[tex]\[
x = 16
\][/tex]
By following the steps, Jen correctly determined that [tex]\( x = 16 \)[/tex]. Now, we need to evaluate the descriptions of Jen's work:
### Description:
1. "Incorrect. She needed to add 100 to both sides instead of subtracting 100."
This statement is incorrect. Subtracting 100 from both sides is a valid step in solving this type of equation.
2. "Incorrect. She needed to multiply both sides by -2 first, then subtract 100."
This statement is also incorrect. It is not necessary to multiply both sides by -2 first; subtracting 100 initially is a valid approach.
3. "Correct. She could have also subtracted 100 from both sides, then divided by [tex]\(-\frac{1}{2}\)[/tex]."
This statement is correct. Another approach could have been to first subtract 100 from both sides and then deal with the coefficient of [tex]\(x\)[/tex] by dividing by [tex]\(-\frac{1}{2}\)[/tex].
4. "Correct. She could have also multiplied both sides by -2 first, then subtracted 100."
This statement is correct as well. Jen could have first multiplied both sides by -2 and then addressed the resulting equation.
### Conclusion:
Based on the analysis, the best descriptions of Jen's work are the third and fourth options:
- Correct. She could have also subtracted 100 from both sides, then divided by [tex]\(-\frac{1}{2}\)[/tex].
- Correct. She could have also multiplied both sides by -2 first, then subtracted 100.
Hence, the correct responses are options 3 and 4.
