# How do you solve 2a-3=-11?

May 30, 2017

$a = - 4$

#### Explanation:

First, identify what needs to be solved.
In this case, we don't know the value of "a".

In equations like these, the element we don't know is usually written as "x", but it doesn't have to be that. In fact, you can use just about every letter you can think of, and the equations would be similar:

Here are some examples of similar equations, that are all solved the same way:

$2 x - 3 = - 11$

$2 b - 3 = - 11$

$2 z - 3 = - 11$

$2 y - 3 = - 11$

All the letters indicate a value we don't know.

Let's return to $2 a - 3 = - 11$
To solve this, we need to find a value of "a", that will make the equation true. To do that we are allowed to make all the operations we want, as long as we do it on both sides of the equal sign, in order to maintain balance and equality.
In a sense, this is basically a small puzzle game.

I'll give one very good tip. It is usually best to "isolate" the part with the letter, in this case "a", first.

To do that let's plus 3 on both sides.
$2 a - 3 = - 11 \iff 2 a - 3 + 3 = - 11 + 3$
This sign "$\iff$" means we have rewritten the equation.
Now we reduce:
$- 3 + 3 = 3 - 3 = 0$
$- 11 + 3 = 3 - 11 = - 8$

Therefore we get:
$2 a = - 8$

Next, we divide with 2 on both sides.
$2 a = - 8 \iff \frac{2 a}{2} = - \frac{8}{2}$

This means:
$\frac{2}{2} = 1$
and
$- \frac{8}{2} = - 4$

Therefore we get:
$a = - 4$

We can check to see if this is correct by replacing "a" with -4 in the original equation.

$2 a - 3 = 2 \cdot \left(- 4\right) - 3 = - 8 - 3 = - 11$

And there you have the solution :)