Algebra help dont understand please help me?

Question

1. Graph on a number line where x is a real number

-3<x lessthan or equal to 3

2. Graph the inequality on a plane

5x+6y lessthan or equal to 30

Answer 1

1)  -3 &lt; x &lt;= 3

These would be the numbers between -3 and 3, including 3 but not including -3.  You&#039;d put an open circle on -3 (to indicate that it&#039;s not a part of the solution set) and a closed circle on 3 (to indicate that it is), then shade in (essentially make a very heavy line on) the numbers between the two.

2)  5x + 6y &lt;= 30

Start by graphing the line 5x + 6y = 30.  I&#039;m going to assume you know how to do that.  You will use a solid line if the line is part of the solution set, as it is here.  You will use a dotted line if it isn&#039;t.  You can tell the line is part of the solution set because it&#039;s &quot;less than OR EQUAL TO&quot;.  Without the &quot;or equal to&quot;, you&#039;d use a dotted line.

Once you have the line, you&#039;ve split the plane into two parts. One side of the line is the solution set you want, the other isn&#039;t.  You&#039;re going to shade in the proper side.  While there are tricks for figuring out which side is which, I find the easiest way to be to pick a point which is not on the line and plug it into the original inequality.  If it works, that&#039;s the right side.  If not, it&#039;s the other side.  I prefer to work with the origin, (0, 0), as that&#039;s almost always the easiest point to use.  In this case, we&#039;d have

5(0) + 6(0) &lt;= 30

0 &lt;= 30

That&#039;s correct, so we&#039;ll shade the side of the line that has the origin on it.