# How do you solve the inequality -2/3 d - 2 < 1/3 d + 8 ?

Apr 8, 2018

$d > - 10$

#### Explanation:

$\text{collect terms in d on one side and numeric values on the}$
$\text{other side of the inequality}$

$\text{add "2/3d" to both sides}$

$\cancel{- \frac{2}{3} d} \cancel{+ \frac{2}{3} d} - 2 < \frac{1}{3} d + \frac{2}{3} d + 8$

$\Rightarrow - 2 < d + 8$

$\text{subtract 8 from both sides}$

$- 2 - 8 < \mathrm{dc} a n c e l \left(+ 8\right) \cancel{- 8}$

$\Rightarrow - 10 < d \text{ or } d > - 10$

Apr 8, 2018

$- 10$<$d$

#### Explanation:

Multiply everything by 3

$- 2 d - 6$<$d + 24$

$- 6$<$3 d + 24$
-30$<$3$d$
$- 10$<$d$