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How do you solve \[\dfrac{2}{3}x-\dfrac{1}{6}=\dfrac{1}{2}x+\dfrac{5}{6}\]?

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Last updated date: 26th Feb 2024
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IVSAT 2024
Answer
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Hint: Multiply both the sides with 6 to remove the fractional terms. Now, rearrange the terms by taking the terms containing the variable x to the L.H.S. and taking all the constant terms to the R.H.S. Use simple arithmetic operations like: - addition, subtraction, multiplication, division whichever needed, to make the coefficient of x equal to 1. Accordingly change the R.H.S. to get the answer.

Complete step by step answer:
Here, we have been provided with the linear equation: - \[\dfrac{2}{3}x-\dfrac{1}{6}=\dfrac{1}{2}x+\dfrac{5}{6}\] and we are asked to solve this equation. That means we have to find the value of x.
Now, we can see that we have 2, 3 and 6 as the denominators of different terms in the given equation. We know that the L.C.M. of these numbers will be 6, so multiplying both the sides with 6 to remove the fractional terms, we get,
\[\Rightarrow 4x-1=3x+5\]
As we can see that the given equation is a linear equation in one variable which is x, so taking the terms containing the variable x to the L.H.S. and taking all the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 4x-3x=1+5 \\
 & \Rightarrow x=6 \\
\end{align}\]

Hence, the value of x is 6.

Note: One may note that we have been provided with a single equation only. The reason is that we have to find the value of only one variable, that is x. So, in general if we have to solve an equation having ‘n’ number of variables then we should be provided with ‘n’ number of equations. Now, one can check the answer by substituting the obtained value of x in the equation provided in the question. We have to determine the value of L.H.S. and R.H.S. separately and if they are equal then our answer is correct.