# How do you solve -3( 2x + 5) \geq 3x + 3?

Mar 26, 2018

$x \le - 2$

#### Explanation:

Start out by using the distributive property and multiply $- 3$ by the numbers in the parentheses.

$- 3 \left(2 x + 5\right) \ge 3 x + 3$

$- 6 x - 15 \ge 3 x + 3$

Now finish simplifying:

$- 6 x - 15 \ge 3 x + 3$

$- 9 x - 15 \ge 3$

$- 9 x \ge 18$

$- x \ge 2$

We want $x$ to be positive, not negative, so we will multiply both sides by $- 1$. But, there's a catch! We need to switch the greater than sign ($>$) to a lesser than sign ($<$) because we did this.

$- x \left(- 1\right) \textcolor{red}{\ge} 2 \left(- 1\right)$

$x \textcolor{red}{\le} - 2$

This means that x is less than or equal to -2.