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‌How‌ ‌do‌ ‌you‌ ‌solve the linear equation:‌ ‌\[7+3x=6x-8\]?‌

seo-qna
Last updated date: 13th Jun 2024
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Answer
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Hint: Rearrange the terms of the given equation by taking the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S. Now, use simple arithmetic operations, like: addition, subtraction, multiplication or division, whichever needed, to simplify the equation. Make the coefficient of x equal to 1 and accordingly change the R.H.S. to get the answer.

Complete step-by-step solution:
Here, we have been provided with the equation: \[7+3x=6x-8\] and we are asked to solve this equation. That means we have to find the value of x.
\[\because 7+3x=6x-8\]
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 the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 3x-6x=-8-7 \\
 & \Rightarrow -3x=-15 \\
\end{align}\]
Dividing both the sides with (-3) and cancelling the common factors, we get,
\[\Rightarrow x=5\]
Hence, the value of x is 5.

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 one variable, that is x. So, in general if 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.