```Question 85721
20.

{{{x<=5}}}

In order to graph this system of inequalities, we need to graph each inequality one at a time.

So lets graph the first inequality

In order to graph {{{x<=5}}} we need to graph the equation {{{x=5}}} (just replace the inequality sign with an equal sign). So lets graph the line {{{x=5}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)

{{{graph( 400, 300, -5, 10, -10, 10,1000(x-5000/1000))}}} graph of {{{x=5}}}

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{x<=5}}}

{{{(0)<=5}}} Plug in x=0, y=0

{{{0<=5}}} Simplify

Since this inequality is true, we shade the entire region containing (0,0)

{{{drawing( 400, 300, -5, 10, -10, 10,graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+0)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+0.75)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+1.5)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+2.25)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+3)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+3.75)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+4.5)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+5.25)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+6)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+6.75)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+7.5)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+8.25)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+9)),
graph( 400, 300, -5, 10, -10, 10,10000(x-5000/1000), 10000(x-5000/1000+9.75)))}}}

Here is the graph of {{{x<=5}}} with the graph of the line({{{x=5}}}) in red and the shaded region in green

(note: In this case, the red line is a solid line. This means the boundaries are included in the region.)
```