The problem is to solve the following equation for $k$: $\frac{k}{3} + 4 - 5k = -2k$

1. Problem Description

The problem is to solve the following equation for $k$:

$\frac{k}{3} + 4 - 5k = -2k$

2. Solution Steps

First, combine the $k$ terms on the left side of the equation:

$\frac{k}{3} - 5k + 4 = -2k$

To combine the $k$ terms, rewrite $5k$ as $\frac{15k}{3}$:

$\frac{k}{3} - \frac{15k}{3} + 4 = -2k$

Combine the fractions:

$\frac{k - 15k}{3} + 4 = -2k$

$\frac{-14k}{3} + 4 = -2k$

Subtract 4 from both sides of the equation:

$\frac{-14k}{3} = -2k - 4$

Multiply both sides of the equation by 3:

$3(\frac{-14k}{3}) = 3(-2k - 4)$

$-14k = -6k - 12$

Add $6k$ to both sides of the equation:

$-14k + 6k = -6k - 12 + 6k$

$-8k = -12$

Divide both sides by -8:

$\frac{-8k}{-8} = \frac{-12}{-8}$

$k = \frac{12}{8}$

Simplify the fraction:

$k = \frac{3}{2}$

3. Final Answer

$k = \frac{3}{2}$