Question 130435: When graphing an inequality for that absolute value of an equation or number, how do you tell which way to graph the solutions( answers)?
Ex:
18-2x<20
Q: How will your number line look when you graph it?
How can you tell which where to plot ?
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! You can always tell by checking one point on the line. Here is a step-by step for your example:
First, pretend you have an equation.
18-2x=20
-2x=2
x=-1
Now look back at the inequality. Since there was a "less than" sign, as opposed to "less than or equal to", put a circle (open dot) at x=-1 on the number line.
Now try a point to the left or right. x=0 is usually an easy one to try. If the inequality remains true (such as 4<5), that is included in the solution. If the inequality is false (such as 5<4), the solution is the other side of the number line.
18-2x<20
18-2(0)<20
18-0<20
18<20
This is true, so 0 is part of the solution. So the number line should have a circle at x=-1, and an arrow to the right.
If you try other points to the right of -1, they will all work. If you try points to the left, they will not.
You also could solve this without plotting points. Just switch the directions of the inequality sign if you multiply or divide by a negative number. Otherwise, keep the sign the same. Here is your example again:
18-2x<20
-2x<2
x>-1
So x can be anything bigger than -1, so the d=shaded arrow would go to the right on the number line.
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