Question

How do you solve $3x+11=7x-5$?

Answer 1

Hint: In this problem we need to calculate the solution for the given equation which is a linear equation in a single variable. For solving this problem, we will apply reverse arithmetic operation for the operations which are in the given equation. So, we will first subtract the term $3x$ from both sides of the above equation. Now we will simplify the equation, after that we will subtract the term $11$ on both sides of the above equation. Now we will simplify the obtained equation to get the required solution.

Complete step-by-step solution:
Given equation, $3x+11=7x-5$.
In the above equation we have $3x$ in addition. So, we are going to subtract the term $3x$ from both sides of the above equation, then we will get
$\Rightarrow 3x+11-3x=7x-5-3x$
We know that $+a-a=0$, then the above equation is modified as
$\Rightarrow 11=4x-5$
In the above equation we have $11$ in addition. So, subtracting the $11$ from both sides of the above equation, then we will get
$\begin{align}
  & \Rightarrow 11-11=4x-5-11 \\
 & \Rightarrow 0=4x-16 \\
\end{align}$
Shifting the $16$ from right hand side to left hand side and changing the sign, then we will have
$\Rightarrow 4x=16$
Dividing the above equation with $4$ on both sides, then the above equation will be
$\begin{align}
  & \Rightarrow \dfrac{4x}{4}=\dfrac{16}{4} \\
 & \Rightarrow x=4 \\
\end{align}$
Hence the solution for the given equation $3x+11=7x-5$ is $x=4$.

Note: We can also check whether the obtained solution is correct or wrong by substituting the obtained value in the given equation, then we will get
$\begin{align}
  & \Rightarrow 3\left( 4 \right)+11=7\left( 4 \right)-5 \\
 & \Rightarrow 12+11=28-5 \\
 & \Rightarrow 23=23 \\
 & \Rightarrow LHS=RHS \\
\end{align}$
Hence the calculated solution is correct.