Question

How do you solve $7x+3=4x-18$?

Answer 1

Hint: The equation given in the question, $7x+3=4x-18$, is in the form of a variable $x$, whose highest power is equal to one. So the given equation is a linear equation which means that it has one solution. Now, for solving the given equation, we first have to separate the variable on the LHS and all the constants on the RHS. For this, the term $4x$ has to be subtracted from both sides and then $3$ has to be subtracted from both sides. Then using the algebraic operations, we will get the final answer.

Complete step by step solution:
The equation in the above question is written as
$\Rightarrow 7x+3=4x-18$
Subtracting $4x$ both the sides of the above equation we get
$\begin{align}
  & \Rightarrow 7x+3-4x=4x-18-4x \\
 & \Rightarrow 3x+3=-18 \\
\end{align}$
Now, we subtract $3$ from both sides of the above equation to get
$\begin{align}
  & \Rightarrow 3x+3-3=-18-3 \\
 & \Rightarrow 3x=-21 \\
\end{align}$
Finally we divide both the sides by $3$ to get the solution as
$\begin{align}
  & \Rightarrow \dfrac{3x}{3}=-\dfrac{21}{3} \\
 & \Rightarrow x=-7 \\
\end{align}$
Hence, the given equation is solved and the obtained solution is $x=-7$.

Note: We can see that the solution of the above question involves only the calculations. So we must carefully carry out all of the calculations in each step, taking proper care of the signs. Also, we must verify the obtained solution by putting it back into the given equation. If we get the LHS equal to RHS, then this means that the obtained solution is correct. But if the LHS does not come equal to the RHS, then this means that there is some error in our calculation.