Question

If \[\dfrac{\left( 2x-1 \right)}{3}=\dfrac{\left( x-2 \right)}{3}+1\], then\[x=\]?
a) 2
b) 4
c) 6
d) 8

Answer 1

Hint:In the given question, we have been have to find the value of x. in order to solve this question, we just to solve the given equation i.e. \[\dfrac{\left( 2x-1 \right)}{3}=\dfrac{\left( x-2 \right)}{3}+1\] by simplifying the equation using only basic mathematical operations such as addition, subtraction, multiplication and division.

Complete step by step solution:
We have given that,
\[\Rightarrow \dfrac{\left( 2x-1 \right)}{3}=\dfrac{\left( x-2 \right)}{3}+1\]
Now, solving this value for the value of\[x\].
Transposing \[\dfrac{\left( x-2 \right)}{3}\] on the left-side of the equation, we obtain
\[\Rightarrow \dfrac{\left( 2x-1 \right)}{3}-\dfrac{\left( x-2 \right)}{3}=1\]
On simplifying the above, we get
\[\Rightarrow \dfrac{\left( 2x-1 \right)-\left( x-2 \right)}{3}=1\]
On further simplification, we get
\[\Rightarrow \dfrac{2x-1-x+2}{3}=1\]
Combining the like terms, we get
\[\Rightarrow \dfrac{x-1+2}{3}=1\]
Combining the numbers, we get
\[\Rightarrow \dfrac{x+1}{3}=1\]
Multiplying both the sides of the equation by 3, we get
\[\Rightarrow x+1=3\]
Subtracting 1 from both the sides of the equation, we get
\[\Rightarrow x+1-1=3-1\]
\[\Rightarrow x=2\]
Therefore, the value of x is equals to 2.
Hence, \[x=2\]
Therefore, option (a) is the correct answer.

Note: In the given question, no mathematical formula is being used; only the mathematical operations such as addition, subtraction, multiplication and division is used.
● Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation.
● Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1.
The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.