Question

How do you solve \[-15x=-30-5x\]?

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 answer:
Solving an equation means we have to find the value of ‘x’ for which the equation gets satisfied.
The given equation, we have \[-15x=-30-5x\]
We have to separate the terms containing ‘x’ and the constant terms.
Bringing all terms containing ‘x’ to the left side of the equation and constant terms to the right side of the equation, we get
\[\begin{align}
  & \Rightarrow -15x+5x=-30 \\
 & \Rightarrow -10x=-30 \\
\end{align}\]
Dividing both the sides by $-10$, we get
\[\Rightarrow \dfrac{-10x}{-10}=\dfrac{-30}{-10}\]
Cancelling out $-10$ both from the numerator and the denominator on the left side and reducing the fraction \[\dfrac{-30}{-10}\] as \[\dfrac{-30}{-10}=\dfrac{3}{1}\] on the right side, we get
$\begin{align}
  & \Rightarrow x=\dfrac{3}{1} \\
 & \Rightarrow x=3 \\
\end{align}$
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 \[\dfrac{-30}{-10}\] that we obtained during the calculation can be reduced. First of all it can be written as \[\dfrac{30}{10}\] (cancelling out the negative sign both from the numerator and the denominator). Then, as we know the common factors of 30 and 10 is $2\times 5$ , so the greatest common factor of 30 and 10 is 10. Hence dividing the numerator and the denominator of \[\dfrac{30}{10}\] by the greatest common factor ‘10’, we get
\[\dfrac{30}{10}=\dfrac{30\div 10}{10\div 10}=\dfrac{3}{1}=3\]