Solve the inequality $2(5 - 3x) - 4x + 6 \ge 0$ for $x$.

1. Problem Description

Solve the inequality $2(5 - 3x) - 4x + 6 \ge 0$ for $x$.

2. Solution Steps

Step 1: Distribute the 2 in the first term.

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

Step 2: Combine like terms.

$-10x + 16 \ge 0$

Step 3: Subtract 16 from both sides.

$-10x \ge -16$

Step 4: Divide both sides by -

1

0. Remember to flip the inequality sign because we are dividing by a negative number.

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

Step 5: Simplify the fraction.

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

3. Final Answer

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