Equations

A mathematical equation is an expression that contains an equals sign and an unknown. The unknown is usually called $ \large x $.

An equation can look like this:

$$ \large x + 6 = 10 $$

Here we ask: what number must $ \large x $ be for the calculation to be correct?

To find $ \large x $ we need it to stand alone on one side of the equals sign. This is called isolating $ \large x $.

In the equation there is $ \large +6 $ together with $ \large x $. To remove $ \large +6 $ we subtract 6 from both sides of the equals sign:

$$ \large x + 6 - 6 = 10 - 6 $$

When we subtract 6, the $ \large +6 $ on the left side disappears, and we get:

$$ \large x = 4 $$

When we write each step in a solution, we use the symbol for "the same as":

$$ \Large \Leftrightarrow $$

This shows that each step is just a rewriting of the same equation.

The solution can therefore be written like this:

$$ \large x + 6 = 10 \Leftrightarrow $$

$$ \large x + 6 - 6 = 10 - 6 \Leftrightarrow $$

$$ \large x = 4 $$

The result is therefore $ \large x = 4 $. We can always check the answer by inserting it into the original equation:

$$ \large 4 + 6 = 10 $$

That is correct.

Now let us look at another type of equation:

$$ \large 2x = 10 $$

Here we need $ \large x $ to stand alone. Right now $ \large x $ is multiplied by 2. To remove this, we divide both sides by 2:

$$ \large \tfrac{2x}{2} = \tfrac{10}{2} $$

This gives:

$$ \large x = 5 $$

We can check the answer by inserting $ \large x = 5 $ into the original equation:

$$ \large 2 \cdot 5 = 10 $$

That is also correct.