The problem asks us to solve the inequality $2(5-3x) - 4x + 6 \ge 0$.

1. Problem Description

The problem asks us to solve the inequality $2(5-3x) - 4x + 6 \ge 0$.

2. Solution Steps

First, distribute the $2$ into the parenthesis:

$2(5-3x) - 4x + 6 \ge 0$

$10 - 6x - 4x + 6 \ge 0$

Next, combine like terms:

$16 - 10x \ge 0$

Then, subtract 16 from both sides of the inequality:

$-10x \ge -16$

Now, divide both sides by -

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0. Since we are dividing by a negative number, we must reverse the inequality sign:

$x \le \frac{-16}{-10}$

$x \le \frac{16}{10}$

$x \le \frac{8}{5}$

3. Final Answer

$x \le \frac{8}{5}$