Question

How do you solve $144 = - 12(x + 5)$?

Answer 1

Hint: The given question is basically a linear equation in one variable. It is an equation that can be written in the form of $ax + b = c$ where $a$, $b$ and $c$ are constants and $x$ is a variable. We will use shortcuts for solving it. One of the basic shortcuts is ‘When a term or expression moves to the other side of the equation, its operation changes to the inverse operation’. The inverse operation for addition is subtraction and vice versa. Also multiplication and division are inverse operations.

Complete step by step solution:
Given equation is $144 = - 12(x + 5)$
We will now send $ - 12$ to the left hand side of the equation. Since $ - 12$ is multiplied to $x + 5$ on the right hand side, so it will be dividing $144$ on the left hand side of the equation.
$ \Rightarrow \dfrac{{144}}{{ - 12}} = x + 5$
$
   \Rightarrow - \dfrac{{144}}{{12}} = x + 5 \\
   \Rightarrow - 12 = x + 5 \\
 $
Now, we will send $5$ to the left hand side of the equation. Since $5$ is added to $x$ on the right hand side, it will be subtracted from $ - 12$ on the left hand side of the equation.
$
   \Rightarrow - 12 - 5 = x \\
   \Rightarrow - 17 = x \\
 $
On rearranging variable to the left hand side and constant on the right hand side, we get
$ \Rightarrow x = - 17$

Hence, the solution for $144 = - 12(x + 5)$ is $x = - 17$.

Note: A lot of people get confused between linear equations and linear expressions. Linear expressions are made up of variables and constants. These are generally joined with the help of algebraic operations (addition, subtraction, division, multiplication, etc.) as per the need of the question. Here is a simple thing to keep in mind so as to avoid any confusion regarding this- “Expressions make Equations”.