# How do you solve the inequality 3t + 1 < t + 12?

Jun 2, 2018

$t < \frac{11}{2}$

#### Explanation:

The key realization here is that, for the most part, we can treat this like an equation. If we had

$3 t + 1 = t + 12$

we would subtract $1$ from both sides, and subtract $t$. We can do the same thing with $3 t + 1 < t + 12$. We get

$3 t < t + 11$

$\implies 2 t < 11$

Dividing both sides by $2$, we get

$t < \frac{11}{2}$

Hope this helps!

Jun 2, 2018

$t < \frac{11}{2}$

#### Explanation:

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

$\text{subtract "t" from both sides}$

$3 t - t + 1 < \cancel{t} \cancel{- t} + 12$

$2 t + 1 < 12$

$\text{subtract 1 from both sides}$

$2 t < 11$

$\text{divide both sides by 2}$

$t < \frac{11}{2} \text{ is the solution}$

$t \in \left(- \infty , \frac{11}{2}\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$