# How do you solve the two step inequality 1/2t + 3/4 > 1/4t?

Apr 30, 2018

$t > - 3$

#### Explanation:

$\text{collect terms in t on the left side of the inequality and}$
$\text{numeric values on the right side}$

$\text{subtract "1/4t" from both sides}$

$\frac{1}{2} t - \frac{1}{4} t + \frac{3}{4} > \cancel{\frac{1}{4} t} \cancel{- \frac{1}{4} t}$

$\Rightarrow \frac{1}{4} t + \frac{3}{4} > 0$

$\text{subtract "3/4" from both sides}$

$\Rightarrow \frac{1}{4} t > - \frac{3}{4}$

$\text{multiply both sides by 4}$

$\Rightarrow t > - 3$

$t \in \left(- 3 , \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$