Let's critically analyze Micah's steps and determine if his conclusion is correct and what the correct form of the solution should be.
1. The original equation to solve is:
[tex]\[
\frac{5}{6}(1 - 3x) = 4\left(-\frac{5x}{8} + 2\right)
\][/tex]
2. To eliminate the fractions, we clear the denominators by multiplying every term by the least common multiple (LCM) of 6 and 8. The LCM of 6 and 8 is 24:
[tex]\[
24 \cdot \frac{5}{6}(1 - 3x) = 24 \cdot 4\left(-\frac{5x}{8} + 2\right)
\][/tex]
3. Multiply and simplify both sides:
[tex]\[
4 \cdot 5(1 - 3x) = 96\left(-\frac{5x}{8} + 2\right)
\][/tex]
[tex]\[
20(1 - 3x) = 96\left(-\frac{5x}{8} + 2\right)
\][/tex]
4. Simplify inside the parentheses:
[tex]\[
20 - 60x = 96\left(-\frac{5x}{8}\right) + 192
\][/tex]
5. Distribute and simplify the right-hand side:
[tex]\[
20 - 60x = -60x + 192
\][/tex]
6. Now, observe that when we simplify the equation further, we notice:
[tex]\[
(20 - 60x) + 60x = (-60x + 192) + 60x
\][/tex]
[tex]\[
20 = 192
\][/tex]
7. This simplifies to a contradiction:
[tex]\[
20 = 192
\][/tex]
Since the simplification leads to a contradiction, it indicates there is no value of \( x \) that satisfies the given equation. Therefore, Micah's solution is incorrect.
Given this detailed analysis, the correct statement about Micah's solution is:
Micah's solution is wrong. There are no values of [tex]\( x \)[/tex] that make the statement true.
