Question

Solve the linear equation $x+7-\dfrac{8x}{3}=\dfrac{17}{6}-\dfrac{5x}{2}$

Answer 1

Hint: By solving the given equation we have to find the value of x. To solve the given equation first we will shift all the constant terms at the RHS and keep the variable terms at the LHS. Then we will simplify the given algebraic operations like addition, subtraction, multiplication and division to get the desired answer.

Complete step by step answer:
We have been given an equation $x+7-\dfrac{8x}{3}=\dfrac{17}{6}-\dfrac{5x}{2}$.
We have to solve the given equation and find the value of the unknown variable x.
As the given equation is a linear equation in one variable. The linear equation in one variable has one unknown variable and it has only one solution. By solving the equation we have to find the value of an unknown variable. In order to solve the given equation first let us shift all the constant terms at the RHS and keep the variable term at the LHS. Then we will get
$\Rightarrow x-\dfrac{8x}{3}+\dfrac{5x}{2}=\dfrac{17}{6}-7$
Now, taking LCM on both sides and simplifying the above obtained equation we will get
$\Rightarrow \dfrac{6x-16x+15x}{6}=\dfrac{17-42}{6}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \dfrac{5x}{6}=\dfrac{-25}{6}$
Now, cancelling out the common terms we will get
$\Rightarrow 5x=-25$
Now, dividing the whole equation by 5 we will get
$\Rightarrow \dfrac{5x}{5}=\dfrac{-25}{5}$
Now, simplifying the above obtained equation we will get
$\Rightarrow x=-5$
Hence by solving the given equation we will get the value of x as $-5$.

Note: As given is the linear equation in one variable. We can verify the answer by putting the obtained value of x in the given equation. As it is a simple question so avoid calculation mistakes. Be careful while shifting the terms from LHS to RHS and vice-versa. Even a single sign mistake also leads to the wrong answer.