Question

How do you solve the linear equation?
$5x-21=8x-30$

Answer 1

Hint: To solve the given equation, we have to rearrange the given equation in such a manner so that on one side of this equation, we will get the expression in $x$ and on the other side of the equation, we will get the constant terms. After that we will do the arithmetic on the equation in such a manner so that the coefficient of $x$ will become 1. And in this way, we can find the solution of x.

Complete step-by-step solution:
The equation given in the above problem is as follows:
$5x-21=8x-30$
And we are asked to solve the above equation. As you can see that the above equation is the linear equation in one variable. Now, you might be thinking how it is a linear equation in one variable, the answer is first of all the degree (highest power of the variable is 1) and secondly, it has only one variable which is $''x''$.
Now, we are going to solve the above equation by rearranging this equation in such a manner so that variable $x$ will present in one side of the equation so we are subtracting $5x$ on both the sides of the above equation and we get,
$\begin{align}
  & -21=8x-5x-30 \\
 & \Rightarrow -21=3x-30 \\
\end{align}$
After that we are going to add 30 on both the sides of the above equation so that constant terms will be on the other side of the equation.
$\begin{align}
  & -21+30=3x \\
 & \Rightarrow 9=3x \\
\end{align}$
Dividing 3 on both the sides of the above equation we get,
$\dfrac{9}{3}=\dfrac{3x}{3}$
In the above equation, 3 will get cancelled out from the numerator and the denominator in the R.H.S of the above equation and in the L.H.S of the above equation, 9 will get divided by 3 by 3 times.
$3=x$
Hence, we have found the solution of the given equation as $x=3$.

Note: You can check the value of $x$ which you are getting is correct or not by substituting this value of $x$ in the given equation and then see whether that value of x is satisfying the given equation or not.
The value of $x$ which we are getting in the above solution is 3 and the equation given above is as follows:
$5x-21=8x-30$
Substituting $x=3$ in the above equation we get,
$\begin{align}
  & 5\left( 3 \right)-21=8\left( 3 \right)-30 \\
 & \Rightarrow 15-21=24-30 \\
 & \Rightarrow -6=-6 \\
\end{align}$
In the above equation, L.H.S = R.H.S so the value of x which we have found in the above solution is correct.