# How do you solve 3(2x-1)>=4(2x-3)-3?

Jan 2, 2017

$x \le 6$

#### Explanation:

Distribute brackets on both sides of the inequality.

$6 x - 3 \ge 8 x - 12 - 3 \Rightarrow 6 x - 3 \ge 8 x - 15$

Collect terms in x on the left side and numeric values on the right side.

subtract 8x from both sides.

$6 x - 8 x - 3 \ge \cancel{8 x} \cancel{- 8 x} - 15$

$\Rightarrow - 2 x - 3 \ge - 15$

$- 2 x \cancel{- 3} \cancel{+ 3} \ge - 15 + 3$

$\Rightarrow - 2 x \ge - 12$

To solve for x, divide both sides by - 2

$\textcolor{b l u e}{\text{Note}}$ when we multiply/divide an inequality by a negative value we must $\textcolor{b l u e}{\text{reverse the inequality sign}}$

$\frac{\cancel{- 2} x}{\cancel{- 2}} \le \frac{- 12}{- 2} \leftarrow \text{ reverse sign}$

$\Rightarrow x \le 6 \text{ is the solution}$