Question

How do you solve for $x:3x+3=-2x-12?$

Answer 1

Hint: We have to find $x$ . And for these kinds of questions, all we need is basic mathematics which is transferring all the unwanted variables and constants to the opposite side of the wanted variable and making the entire equation as a function of the wanted variable.

Complete step by step answer:
Let us consider, we have, $s=ax+b$ and we want to find $x$ from this equation. We have $s=ax+b$ . We will transfer $b$ which is our constant in this expression and $a$ which is the coefficient of our $x$ term to the other side which has $s$ . We get the following :
$\Rightarrow \dfrac{s-b}{a}=x$ . Now this became a function of $x$ and we got our $x$ .
In the same way , let’s find out the value of $x$ from the above given question .
We have to convert the given question into a function of $x$ .
So now let’s shift the $-2x$ to the left hand side of the equation while keeping the $-12$ on the right hand side itself. Upon doing so , we get the following :
$\Rightarrow 3x+2x+3=-12$
Now let’s shift the $-3$ to the right hand side of the equation. Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 5x=-12-3 \\
 & \Rightarrow 5x=-15 \\
 & \Rightarrow x=-3 \\
\end{align}$
If you observe carefully, all we did here is to just group all the variable terms to one side and all the constant terms on the other side. Since we have only one variable which is $x$ , we need only one equation to solve for it. But , in case , we have two variables to solve, we will definitely require two equations to solve for both the variables.

$\therefore $ Hence the value of $x$ upon solving $3x+3=-2x-12$ is $-3$

Note: We have to be careful while shifting terms. And we have to be alert with the sign as they may lead to calculation errors. Always group the like variable terms together and constants on the other side of the equation.