# How do you solve 4( x + 1) - 5x - 4= 9?

Oct 3, 2016

$x = - 9$

#### Explanation:

We are trying to solve for $x$ which is an unknown variable. If you plug $x$ (after you solve it) back into the equation then one side of the equation should equal the other side. $\left(9 = 9\right)$

In algebra we go by the PEMDAS rule. Parenthesis first. You can do this by using the distributive property.

$4 \left(x + 1\right) - 5 x - 4 = 9$

Remember distributive property is multiplying what is outside the parenthesis by what is inside. So $4$ times $x$ is $4 x$ and $4$ times $1$ is $4$. You write this out and what is left over that you haven't solved yet.

$4 x + 4 - 5 x - 4 = 9$

This is what we have so far. Now we can either add up like terms (every number with an $x$ attached to it), or add constants (regular plain numbers without $x$ attached to it) or if you're really pro you can do both at the same time.

So like terms first:

$4 x - 5 x$ is the same thing as $4 - 5$ which is $- 1$, so you get

$- 1 x + 4 - 4 = 9$

Now constants: $4 - 4 = 0$ so you don't have to write anything it just disappears, it's zero!

Now what we have so far is

$- 1 x = 9$

And what we do next is divide $- 1 x$ by $- 1$ and then divide the number on the other side (in this case $9$) also by $- 1$. Therefore

$\frac{\cancel{- 1} x}{\cancel{- 1}} = \frac{9}{- 1}$

When we solve this $\left(\frac{9}{- 1}\right)$ we get $- 9$, so $- 9$ is the answer.

$x = - 9$

Like I said at the beginning, if you plug $- 9$ back into the equation, if your problem solving was right, then one side should equal the other one. And when we plug $- 9$ into the parenthesis and solve the left side of the equation, $9 = 9$, so we know for sure our answer is right.

Happy hunting!