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

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answer is A.

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Detailed Solution

Given,

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

.
Solve the equation for x.

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

The LCM between any number with 1 is the number itself.

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

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

x - 2 = 2 x - 4

2 x - x = 4 - 2

x = 2

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

\frac{x - 2}{3}

= \frac{2 - 2}{3}

= 0

RHS =

\frac{2 x - 1}{3} - 1

= \frac{2 \times 2 - 1}{3} - 1 = 0

LHS = RHS
So, the value of x is 2.
Hence, option 1 is correct.

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