IDNLearn.com connects you with experts who provide accurate and reliable answers. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.
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.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.