Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
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.
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.
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.