How do you solve and graph 5-(x+4)<= -3?

Jul 25, 2018

$x \ge 4$

Explanation:

$5 - \left(x + 4\right) \le - 3$

Distribute the negative sign on the left side:
$5 - x - 4 \le - 3$

Simplify:
$1 - x \le - 3$

Add $\textcolor{b l u e}{x}$ to both sides:
$1 - x \quad \textcolor{b l u e}{+ \quad x} \le - 3 \quad \textcolor{b l u e}{+ \quad x}$

$1 \le - 3 + x$

Add $\textcolor{b l u e}{3}$ to both sides:
$1 \quad \textcolor{b l u e}{+ \quad 3} \le - 3 + x \quad \textcolor{b l u e}{+ \quad 3}$

$4 \le x$

Therefore,
$x \ge 4$

Here's a graph of it on a number line:

(mathwarehouse.com)

The closed circle on $4$ means that it is a solution (and anything greater than it is).

Hope this helps!