# How do you solve  3+ 5t < 3(t + 1)-4(2 - t)?

May 27, 2017

Answer: $\left(4 , \infty\right)$

#### Explanation:

Solve $3 + 5 t < 3 \left(t + 1\right) - 4 \left(2 - t\right)$

First, let us expand everything and combine like-terms on each side:
$3 + 5 t < 3 t + 3 - 8 + 4 t$

$3 + 5 t < 7 t - 5$

Now, we can subtract $5 t$ and add $5$ to both sides:
$3 + 5 t - 5 t + 5 < 7 t - 5 - 5 t + 5$

And simplify:
$8 < 2 t$

Finally, we divide both sides by $2$:
$\frac{8}{2} < \frac{2 t}{2}$
$4 < t$
or
$t > 4$

which we can also write in interval notation as $\left(4 , \infty\right)$