# How do you simplify -6(7 + x)?

May 7, 2016

$- 42 - 6 x$

#### Explanation:

$\textcolor{b l u e}{\text{Detailed explanation building up to the shortcut method}}$

When it is written in the form $- 6 \left(7 + x\right)$ it is the same as $\left(- 6\right) \times \left(7 + x\right)$

I will deal with the negative aspect of this in a while.

This means that you have 6 lots of $\left(7 + x\right)$

So you have 6 lots of 7 and $6 \times 7 = 42$

You also have 6 lots of x and $6 \times x = 6 x$

So, ignoring the negative part of -6,

$6 \left(7 + x\right) = 42 + 6 x$

$\textcolor{b r o w n}{\text{Everything inside the bracket is multiplied by 6}}$

$\textcolor{b r o w n}{\text{However, we have } - 6 \left(7 + x\right)}$

This is the same as $\left(- 1\right) \times 6 \times \left(7 + x\right)$

Multiply everything inside the bracket by $\left(- 1\right)$ giving:

$6 \times \left(- 7 - x\right)$

Now multiply everything inside the bracket by 6 giving:

$- 42 - 6 x$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Shortcut method}}$

Given: $- 6 \left(7 + x\right)$

$\textcolor{b r o w n}{\text{Multiply everything inside the bracket by -6}}$

$- 42 - 6 x$