Question

Solve the given equation and find the value of x. The equation is \[2x-1=14-x\] .

Answer 1

Hint: Take all the variable terms of x in LHS and constants to the RHS of the equation. In this equation, just take the -x term to LHS and -1 to RHS and solve it further.

Complete step-by-step answer:
According to the question, we have a linear equation. In that linear equation, we have a variable x which is unknown. We have to find the value of x using the given equation.
We have,
\[2x-1=14-x\]…………(1)
In LHS we have unknown variable x terms and constant terms.
Similarly, we have variable x terms and constant terms in RHS of the equation.
So, our target is to make one side of the equation to have only unknown variable x terms.
In equation(1), taking the term -x to the LHS, we get
\[2x-1+x=14\]……………….(2)
Now, in the equation (2), taking -1 to the RHS, we get
\[\begin{align}
  & 2x+x=14+1 \\
 & \Rightarrow 3x=15 \\
 & \Rightarrow x=\dfrac{15}{3} \\
 & \Rightarrow x=5 \\
\end{align}\]
Hence, the value of x is 5.

Note: In this question, one can make mistakes in taking -x of RHS to the LHS and write -x in LHS too, which is wrong. If we are moving some terms of RHS to LHS then its sign is changed and vice-versa. Here we are moving -x to the LHS. So, we have to write +x in the LHS of the equation. Similarly, we are moving -1 of LHS to the RHS. So, we have to write +1 in the RHS of the equation.