# How do you solve 19 < 7 + 1/3k + 2 -2/3k?

May 12, 2015

Solve $19 < 7 + \frac{1}{3} k + 2 - \frac{2}{3} k$ .

Combine like terms.

$19 < 7 + 2 + \frac{1}{3} k - \frac{2}{3} k$ =

$19 < 9 - \frac{1}{3} k$

Simplify $\frac{1}{3} k$ to $\frac{k}{3}$.

$19 < 9 - \frac{k}{3}$

Multiply both sides times $3$.

$19 \cdot 3 < 9 \cdot 3 - k$ =

$57 < 27 - k$

Subtract #27 from both sides.

$57 - 27 < 27 - 27 - k$ =

$30 < - k$

Multiply both sides times $- 1$. This will cause the inequality to be reversed.

$- 30 > k$

Flip to get $k$ on the left side.

$k < - 30$