Question

Solve the following for value of x: $5x-1=3x+5$

Answer 1

We have an expression which we have to solve for $x$. We will have to separate the constant terms and $x$ terms first. We will first subtract $3x$ from both the sides. Then, we will add 1 on both sides, we will have the equation as $2x=6$. Solving further, we will get the value of $x$.

Complete step by step solution:
According to the given question, we have an expression from which we have to find the value of $x$.
The expression we have is,
$5x-1=3x+5$----(1)
Firstly, we will subtract $3x$ from both the sides, we get,
$\Rightarrow 5x-1-3x=3x+5-3x$
On rearranging we get,
$\Rightarrow 5x-3x-1=3x-3x+5$
Solving the above expression, we have,
$\Rightarrow 2x-1=5$
Now, we will add 1 to both the sides and we will get,
$\Rightarrow 2x-1+1=5+1$
Solving the above expression, we will have,
$\Rightarrow 2x=6$
We will now divide both the sides by 2, we get the expression as,
$\Rightarrow \dfrac{2x}{2}=\dfrac{6}{2}$
On solving further, we get,
$\Rightarrow x=3$
Therefore, the value of $x=3$.

Note: Carrying out the calculation step wise gives a clear picture of the solution. Also, we can check if the answer that we obtained is the value of $x$, whether it is correct or not. For that, we will simply substitute the value of $x$ in the given expression and see if the LHS=RHS.
The expression we have is,
$5x-1=3x+5$
We will first take the LHS,
$5x-1$
Substituting the value of $x=3$
$\Rightarrow 5(3)-1$
$\Rightarrow 15-1=14$
Now, we will take the RHS,
$3x+5$
Substituting the value of $x=3$
$\Rightarrow 3(3)+5$
$\Rightarrow 9+5=14$
Since, LHS=RHS,
Therefore, the value of $x=3$ is correct.