# How do you solve x + 8 - 1> x/3 ?

May 24, 2016

$x > - \frac{21}{2}$

#### Explanation:

Given,

$x + 8 - 1 > \frac{x}{3}$

Simplify the left side.

$x + 7 > \frac{x}{3}$

Multiply both sides by $3$.

$\textcolor{red}{3 \left(\textcolor{b l a c k}{x + 7}\right)} > \textcolor{red}{3 \left(\textcolor{b l a c k}{\frac{x}{3}}\right)}$

Simplify.

$3 x + 21 > x$

Subtract $3 x$ from both sides.

$3 x \textcolor{w h i t e}{i} \textcolor{red}{- 3 x} + 21 > x \textcolor{w h i t e}{i} \textcolor{red}{- 3 x}$

$21 > - 2 x$

Divide both sides by $- 2$

$\textcolor{red}{\frac{\textcolor{b l a c k}{21}}{-} 2} > \textcolor{red}{\frac{\textcolor{b l a c k}{- 2 x}}{-} 2}$

$x < - \frac{21}{2}$

Since you divided by a negative number, flip the inequality sign.

$x > \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{- \frac{21}{2}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$