Question

How do you solve $2x-3+4x=21$?

Answer 1

Hint: First separate the constants and variables. Bring all the terms containing ‘x’ to the left side of the equation and the constant terms to the right side of the equation. Then do the necessary calculations to obtain the required result.

Complete step-by-step solution:
Solving an equation means we have to find the value of ‘x’ for which the equation gets satisfied.
The given equation, we have $2x-3+4x=21$
We have to separate the terms containing ‘x’ and the constant terms.
Since all terms containing ‘x’ are already on the left side of the equation, so bringing the constant terms to the right side of the equation, we get
$\begin{align}
  & \Rightarrow 2x+4x=21+3 \\
 & \Rightarrow 6x=24 \\
\end{align}$
Dividing both the sides by 6, we get
$\Rightarrow \dfrac{6x}{6}=\dfrac{24}{6}$
Cancelling out 6 both from the numerator and the denominator on the left side and reducing the fraction $\dfrac{24}{6}$ as $\dfrac{24}{6}=\dfrac{4}{1}$ on the right side, we get
$\begin{align}
  & \Rightarrow x=\dfrac{4}{1} \\
 & \Rightarrow x=4 \\
\end{align}$
This is the required solution of the given question.

Note: Separating the constants and variable terms should be the first approach for solving such questions. The fraction $\dfrac{24}{6}$ that we obtained during the calculation can be reduced. As we know the common factors of 24 and 6 are $2\times 3$, so the greatest common factor of 24 and 6 is 6. Hence dividing the numerator and the denominator of $\dfrac{24}{6}$ by the greatest common factor ‘6’, we get
$\dfrac{24}{6}=\dfrac{24\div 6}{6\div 6}=\dfrac{4}{1}=4$.
So the value of ‘x’ we got $x=4$.