Curry Goodwin
09/20/2023 · Junior High School
Exercises: Solve for \( \mathrm{x}: \) 1. \( \frac{1}{4}=\frac{3}{x}-\frac{1}{2} \) 2. \( \frac{x}{5}=15-\frac{x}{3} \)
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Solve the equation \( \frac{1}{4}=\frac{3}{x}-\frac{1}{2} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{1}{4}=\frac{3}{x}-\frac{1}{2}\)
- step1: Find the domain:
\(\frac{1}{4}=\frac{3}{x}-\frac{1}{2},x\neq 0\)
- step2: Swap the sides:
\(\frac{3}{x}-\frac{1}{2}=\frac{1}{4}\)
- step3: Move the constant to the right side:
\(\frac{3}{x}=\frac{1}{4}+\frac{1}{2}\)
- step4: Add the terms:
\(\frac{3}{x}=\frac{3}{4}\)
- step5: Rewrite the expression:
\(x=4\)
- step6: Check if the solution is in the defined range:
\(x=4,x\neq 0\)
- step7: Find the intersection:
\(x=4\)
Solve the equation \( \frac{x}{5}=15-\frac{x}{3} \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x}{5}=15-\frac{x}{3}\)
- step1: Multiply both sides of the equation by LCD:
\(\frac{x}{5}\times 15=\left(15-\frac{x}{3}\right)\times 15\)
- step2: Simplify the equation:
\(3x=225-5x\)
- step3: Move the variable to the left side:
\(3x+5x=225\)
- step4: Add the terms:
\(8x=225\)
- step5: Divide both sides:
\(\frac{8x}{8}=\frac{225}{8}\)
- step6: Divide the numbers:
\(x=\frac{225}{8}\)
The solutions to the given equations are:
1. \( x = 4 \)
2. \( x = \frac{225}{8} \) or \( x = 28.125 \)
Quick Answer
1. \( x = 4 \)
2. \( x = \frac{225}{8} \) or \( x = 28.125 \)
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