Question

practice: solve rational equations
score: 1/6 answered: 1/6
question 2
solve the equation \\(\frac{5}{8} = \frac{1}{2x - 1}\\)
\\(x = \square\\)
write your answer as a reduced fraction, no decimals are accepted.

Explanation:

Step1: Cross - multiply the equation

To solve the rational equation \(\frac{5}{8}=\frac{1}{2x - 1}\), we use cross - multiplication. Cross - multiplication means that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\).
Applying this to our equation, we get \(5\times(2x - 1)=8\times1\).

Step2: Expand and simplify the left - hand side

Expand \(5\times(2x - 1)\) using the distributive property \(a(b + c)=ab+ac\) (here \(a = 5\), \(b=2x\), \(c=- 1\)). So, \(5\times2x-5\times1 = 10x-5\).
Our equation becomes \(10x - 5=8\).

Step3: Solve for \(x\)

First, add 5 to both sides of the equation: \(10x-5 + 5=8 + 5\).
Simplifying both sides, we have \(10x=13\).
Then, divide both sides by 10: \(x=\frac{13}{10}\).

Answer:

\(\frac{13}{10}\)