Phillips Burns
02/07/2023 · Senior High School
Question 2 \( \frac{1}{4} x+\frac{1}{5}=5\left(\frac{3}{4} x-3\right) \) Solve for \( x \) : You can enter your answer as an improper fraction (like 13/4), but not as a mixed \( x=\square \)
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Step-by-step Solution
Solve the equation \( \frac{1}{4}x+\frac{1}{5}=5\left(\frac{3}{4}x-3\right) \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{1}{4}x+\frac{1}{5}=5\left(\frac{3}{4}x-3\right)\)
- step1: Expand the expression:
\(\frac{1}{4}x+\frac{1}{5}=\frac{15}{4}x-15\)
- step2: Move the variable to the left side:
\(\frac{1}{4}x+\frac{1}{5}-\frac{15}{4}x=-15\)
- step3: Subtract the terms:
\(-\frac{7}{2}x+\frac{1}{5}=-15\)
- step4: Move the constant to the right side:
\(-\frac{7}{2}x=-15-\frac{1}{5}\)
- step5: Subtract the terms:
\(-\frac{7}{2}x=-\frac{76}{5}\)
- step6: Change the signs:
\(\frac{7}{2}x=\frac{76}{5}\)
- step7: Multiply by the reciprocal:
\(\frac{7}{2}x\times \frac{2}{7}=\frac{76}{5}\times \frac{2}{7}\)
- step8: Multiply:
\(x=\frac{152}{35}\)
The solution to the equation \( \frac{1}{4}x+\frac{1}{5}=5\left(\frac{3}{4}x-3\right) \) is \( x=\frac{152}{35} \) or \( x=4.3\dot{4}2857\dot{1} \).
Quick Answer
\( x=\frac{152}{35} \)
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