Question

How do you solve \[\dfrac{1}{2}\left( x-3 \right)+\dfrac{3}{2}-x=5x\] ?

Answer 1

Hint: In the above question we have to find the value of x by solving the equation given. Since the equation has only one variable and it is linear therefore, we can simplify it by performing simple operations. In the case of linear equations in two variables, we require two different equations to get the values of the two variables and in order to solve linear equations in two variables we have elimination method and substitution method. So first we will isolate the variable on one side and the constant term on the other side. Then we will simplify further to get the answer.

Complete step by step answer:
In the above question we have \[\dfrac{1}{2}\left( x-3 \right)+\dfrac{3}{2}-x=5x\] . It is a linear equation in one variable. It is an equation with one variable and degree equal to one. It is also called a two step equation. Linear equation in one variable has only one solution.
Now in the given question we have \[\dfrac{1}{2}\left( x-3 \right)+\dfrac{3}{2}-x=5x\] so, first we will isolate the constant term.
Therefore, we will get.
\[\begin{align}
  & \dfrac{1}{2}\left( x-3 \right)+\dfrac{3}{2}-x=5x \\
 & \Rightarrow \dfrac{x}{2}-\dfrac{3}{2}+\dfrac{3}{2}-x-5x=0 \\
 & \Rightarrow \dfrac{x}{2}-x-5x=0 \\
\end{align}\]
Now on further simplification we will get,
\[\begin{align}
  & \dfrac{x}{2}-x-5x=0 \\
 & \Rightarrow x-2x-10x=0 \\
 & \Rightarrow -11x=0 \\
 & \Rightarrow x=0 \\
\end{align}\]
Therefore, the value of x is equal to \[x=0\] .

Note:
While simplifying the above equation don’t jump directly to the answer. Solve it step by step in order to avoid questions. Keep check of the signs. Check whether the answer is correct or not by substituting the value we got for x in the equation given in the question. Avoid silly mistakes.