Question

How do you solve \[2x-\dfrac{6}{4}=-7\]?

Answer 1

Hint: Multiply both the sides of the equation with 4 to get rid of the fraction. Now, rearrange the terms of the equation by leaving the terms containing the variable x in the L.H.S. while taking the constant terms to the R.H.S. Now, apply the simple arithmetic operations like: - addition, subtraction, multiplication, division, whichever needed, to simplify the equation. Make the coefficient of x equal to 1 to get the answer.

Complete step by step answer:
Here, we have been provided with the equation: \[2x-\dfrac{6}{4}=-7\] and we are asked to solve this equation. That means we have to find the value of x.
\[\because 2x-\dfrac{6}{4}=-7\]
Multiplying both the sides with 4 to remove the fractional term, we get,
\[\Rightarrow 8x-6=-28\]
As we can see that the given equation is a linear equation in one variable which is x. So, leaving the terms containing the variable x in the L.H.S. and taking the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 8x=6-28 \\
 & \Rightarrow 8x=-\left( 28-6 \right) \\
 & \Rightarrow 8x=-22 \\
\end{align}\]
Dividing both the sides with 8, we get,
\[\Rightarrow \dfrac{8x}{8}=\dfrac{-22}{8}\]
Cancelling the common factors on both the sides, we get,
\[\Rightarrow x=\dfrac{-11}{4}\]
Hence, the value of x is \[\dfrac{-11}{4}\].

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.