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What is the value of x in $5 x - \frac{3}{4} = 2 x - \frac{2}{3}$ ?

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\frac{1}{21}

\frac{1}{3}

\frac{1}{36}

\frac{1}{27}

answer is C.

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Detailed Solution

Given,

5 x - \frac{3}{4} = 2 x - \frac{2}{3}

.
Solve the equation for the value of x.

5 x - \frac{3}{4} = 2 x - \frac{2}{3}

5 x - 2 x = \frac{3}{4} - \frac{2}{3}

3 x = \frac{3}{4} - \frac{2}{3}

Prime factorisation of 4 is

2 \times 2

.
Prime factorisation of 3 is 3.
LCM between 3 and 4 is 12.

3 x = \frac{3}{4} - \frac{2}{3}

3 x = \frac{3 \times 3 - 2 \times 4}{12}

3 x = \frac{1}{12}

x = \frac{1}{36}

LHS =

5 x - \frac{3}{4}

= 5 \times \frac{1}{36} - \frac{3}{4}

= \frac{- 11}{18}

RHS =

2 x - \frac{2}{3}

= \frac{- 11}{18}

LHS = RHS.
So, the value of x is

\frac{1}{36}

.
Hence, option 3 is correct.

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