How do you solve 9y-4(y+5)=40?

Aug 1, 2015

This equation has one variable $\left(y\right)$; also called an unknown.

Solving this equation means to find all the real values that $y$ can assume.

Explanation:

Here are the steps that you can follow to get the value(s) of $y$:

$\text{Step 1 :}$ Open the brackets.

This means the you multiply the number outside the brakets$\left(\textcolor{red}{- 4}\right)$ by every terms that's in the brackets : (color(red)y and color(red)5)

So, $- 4 \left(y + 5\right)$ becomes $- 4 \cdot y + \left(- 4\right) \cdot 5 \textcolor{\mathmr{and} a n \ge}{=} - 4 y - 20$

Now we can write $9 y - 4 \left(y + 5\right) = 40 \text{ }$ as $\text{ } 9 y \textcolor{\mathmr{and} a n \ge}{- 4 y - 20} = 40$
$\implies 5 y - 20 = 40$

• Why is $9 y - 4 y = 5 y$?
• Answer : Compare $9 y - 4 y$ to "nine yens minus four yens". The result is five yens. It's the exact same thing.

$\text{Step 2 :}$ Group similar terms together.

Add $20$ on both sides.
Result : $5 y - 20 + 20 = 40 + 20$
$\implies 5 y = 60$

$\text{Step 3 :}$ Nos that you have grouped the like the terms. Make $y$ to be alone on one side.

Divide both sides by $5$

Result : $\frac{5 y}{5} = \frac{60}{5}$

$\implies \textcolor{b l u e}{y = 12}$