SOLUTION: Please help with graph and interval notation?...I am truly stuck! 3(x-3)> -8 the greater than symbol has a line underneath also, -2<3x-5<.

Question 622995: Please help with graph and interval notation?...I am truly stuck! 3(x-3)> -8 the greater than symbol has a line underneath also, -2<3x-5<.
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
PROBLEM 1.
Solving inequalities is a lot like solving equations. We'll go through this step by step.
.

.
First, distribute the 3 across the parentheses. 3(x-3) is 3x-9.

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Add 9 to both sides of the inequality to get 3x by itself on the left hand side. Simplify.

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Divide both sides of the inequality by 3 to isolate the variable x.

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Now we know that x can be any number that is greater than or equal to 1/3. This website doesn't have a way that I've found to graph a number line with a solution, so I'll explain what it looks like.
.
Draw a number line like this one. The filled in circle at 1/3 means that 1/3 is part of the solution.

Now draw a thick arrow on the number line from the filled in circle and to the right. This means that all numbers greater than 1/3 are also part of the solution.
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The solution in interval notation is this: [1/3, ∞). The square bracket on the left means that 1/3 is included. The curved parenthesis mark on the right always goes after infinity. It means that there is no end to the numbers in the solution.
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Here is a nice link about number lines and interval notation:
http://www.mathsisfun.com/sets/intervals.html
.
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I'm looking at your second problem. I'm not sure what you mean by the second < sign. Check the problem carefully. It seems like a typo. You may be able to work it on you own by following the steps above. Email me with any questions or if you get stuck. I'll help you out.
Hope this helps!
.
Ms.Figgy
math.in.the.vortex@gmail.com
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