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

Jul 28, 2016

$x = \frac{4}{3}$

#### Explanation:

$\textcolor{red}{\text{Using first principles method}}$

Given:$\text{ } \textcolor{b r o w n}{- 1 + x = \frac{1}{3}}$

$\textcolor{b r o w n}{- 1 \textcolor{b l u e}{+ 1} + x = \frac{1}{3} \textcolor{b l u e}{+ 1}}$

But $- 1 + 1 = 0 \text{ and } \frac{1}{3} + 1 = \frac{1}{3} + \frac{3}{3} = \frac{4}{3}$

$= 0 + x = \frac{4}{3}$

$x = \frac{4}{3}$

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$\textcolor{red}{\text{Using shortcut method}}$

move the $- 1$ to the other side of the = and change its sign

$\textcolor{b r o w n}{- 1 + x = \frac{1}{3}} \textcolor{b l u e}{\text{ "->" } x = \frac{1}{3} + 1}$

But 1 is the same as $\frac{3}{3}$

$x = \frac{1}{3} + \frac{3}{3} = \frac{4}{3}$