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What is the value of x in $\frac{2 x - 1}{3} - \frac{6 x - 2}{5} = \frac{1}{3}$ ?

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\frac{1}{2}

\frac{1}{5}

\frac{1}{4}

\frac{1}{3}

answer is A.

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Detailed Solution

Given,

\frac{2 x - 1}{3} - \frac{6 x - 2}{5} = \frac{1}{3}

.
Solve the equation for x.

\frac{2 x - 1}{3} - \frac{6 x - 2}{5} = \frac{1}{3}

The LCM between 3 and 5 is 15 since they are primes. For primes their product is the LCM.

\frac{5 (2 x - 1) - 3 (6 x - 2)}{15} = \frac{1}{3}

\frac{10 x - 5 - 18 x + 6}{5} = 1

\frac{- 8 x + 1}{5} = 1

-8x = 4

x = \frac{- 1}{2}

Check whether the solution is correct or not by substitution method.
LHS =

\frac{2 (\frac{- 1}{2}) - 1}{3} - \frac{6 (\frac{- 1}{2}) - 2}{5}

= \frac{1}{3}

RHS =

\frac{1}{3}

LHS = RHS
So, the value of x is

\frac{- 1}{2}

.
Hence, option 1 is correct.

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