# How do you solve -x-3=1?

Jan 26, 2016

$x = - 4 , - x = 4$

#### Explanation:

$- x - 3 = 1$

$\rightarrow - x - 3 = 1$

$\rightarrow - x = 1 + 3 = 4$

$S o , - x = 4 , x = - 4$

Feb 3, 2016

A very slightly different way of saying the same thing!

$x = - 4$

#### Explanation:

Given: $- x - 3 = 1$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Objective}}$

$\textcolor{b r o w n}{\text{To end up with ( +x ) on one side of the equals sign and everything}}$$\textcolor{b r o w n}{\text{else on the other side.}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Multiply everything by (-1)}}$

$+ x + 3 = - 1$

$\textcolor{b l u e}{\text{Subtract 3 from both sides}}$

$x + 3 - 3 = - 1 - 3$

$x + 0 = - 4$

$x = - 4$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{p u r p \le}{\text{Shortcut method}}$

Given: $- x - 3 = 1$

Using the rule that for + or - swapping sides of the equals sign changes the sign of the value.

$x = - 3 - 1$

$x = - 4$