Question

Solve the following for value of x: \[5x-1=3x+5\]

Answer 1

Hint: 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.