# How do you solve the inequality -15 <= c/-4 - 15?

Jan 1, 2016

The solution set is: $S = \left\{c \in \mathbb{R} | c \le 0\right\}$

#### Explanation:

In this specific case, we first make the inequality easier, simplifying it:
$- 15 \le \frac{c}{-} 4 - 15$ multiply it by 4: $- 60 \le \frac{c}{-} 1 - 60$
$\frac{c}{-} 1 = - c$. So, we pass the $- 60$ to the other side of the inequality and solve it:

$- 60 + 60 \le - c$
$0 \le - c$

In order to make the $c$ to be positive, just multiply it by -1. But, when this is made, the inequality signal is reversed - If it is $<$, becomes $>$, etc. Now, in this case:

$0 \le - c$ multiplied by $- 1$:
$0 \ge c$
$c \le 0$

So, the solution set is: $S = \left\{c \in \mathbb{R} | c \le 0\right\}$