Let's analyze Joelle's proportion:
The proportion given is:
[tex]\[
\frac{4}{6} = \frac{5}{x}
\][/tex]
To determine if this proportion is correct, we should verify if both sides of the proportion are indeed equal when we substitute a specific value for [tex]\( x \)[/tex].
Let's break it down step-by-step.
1. Calculate the value on the left side of the proportion:
[tex]\[
\frac{4}{6} = \frac{2}{3} \approx 0.6667
\][/tex]
2. Let’s assume that [tex]\( \frac{5}{x} \)[/tex] should also equal [tex]\(\frac{2}{3}\)[/tex]:
[tex]\(\frac{5}{x} = \frac{2}{3} \)[/tex]
To solve for [tex]\( x \)[/tex], we cross-multiply:
[tex]\[
4x = 6 \times 5
\][/tex]
Simplifying the right side:
[tex]\[
4x = 30
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{4} = 7.5
\][/tex]
3. Now let's check if this is consistent with the original values given:
[tex]\[
\frac{5}{x} = \frac{5}{7.5} \approx 0.6667
\][/tex]
4. Firstly, we identified that the right side had indeed not the value [tex]\(\approx 0.6667\)[/tex], making the given proportional incorrect overall. Let's verify accordingly no inconsistencies lie ahead.
Upon examination of what happened in problem steps:
- The setup proportion fundamentally was not equivalent when approached by looking up individual factions relatively across sides.
Therefore, our original comparison evidenced miscalibraction fairly. Let's summarize Joelle's setup:
[tex]\[
\frac{4}{6}\neq \frac{5}{x}, x
\][/tex]
Given the above discrepancy, stated correctly current option:
- Choice A -> Incorrect
- Demonstrated B assumption arguments entail proving missetup.
Choosing:
- Joelle's proportion inferred incorrect leading diagnostic result exhibited in resolution!.
Conclusively not purely correct according examined based.
Let's validate outcomes:
- Joelle ratio mismatch proportions hence wrong setup as summarized follows."
Final answer:
[tex]\(\boxed{\text{B}}\)[/tex]
Thanks validating!
