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Solving and Graphing Inequalities using Multiplication or Division  Problem 2
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
As is the case when solving equations, when x is in the numerator, this means that x is being divided by the value in the denominator. To undo what is being done to x, do the opposite  multiply by the value. Once the variable is isolated, graph the inequality on a number line. When graphing, keep in mind when to use an open circle versus a closed circle, and which direction the arrow should be pointing.
Remember that when you are working with inequalities and you're solving them, it's almost exactly like solving equations except for sometimes you need to change the direction of the inequality.
Let's check this one out.
I have x divided by 4 is less than or equal to 8. Be really careful that when you see this fraction problem you don't just skip it, come on guys you can totally do this. If you want to you could treat this as 1/4 times x, that's the same thing or the way I think of it is as x divided by 4. The opposite of dividing by 4 would be to multiply both sides by 4 and so now I'm left with x is less than or equal to 32.
Now there's a negative involved in this problem so I want to just double check and see if I need to change the direction, let's see. You would change the sign if you multiplied or divided by a negative value but I didn't. I multiplied by a +4. So this sign stays the same. This is my final answer x is less than or equal 32.
Let's go ahead and draw it on the number line, 32 I'm going to put a closed circle because that's a less than or equal to, and then I want to mark all x values that are smaller than 32. Smaller numbers are out there to the left that means I could use 50, 100, 32.5 or even 32. Any one of those values would work when I substitute it into this original inequality in the x place.
So again guys, this is kind of a trick problem because there is some multiplying and dividing going on and there is a negative number but it's not the number I'm solving with. It's not the number I'm dividing or multiplying by. Just be really careful that you only change the sign if you multiply or divide by a negative value.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”
Sample Problems (3)
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Solving and Graphing Inequalities using Multiplication or Division
Problem 1 7,918 viewsSolve the inequality and graph your solution.
3x < 9 
Solving and Graphing Inequalities using Multiplication or Division
Problem 2 6,672 viewsSolve the inequality and graph your solution.
x ≤ 8 4 
Solving and Graphing Inequalities using Multiplication or Division
Problem 3 5,847 viewsYou have $15 to spend on text messages. In your phone plan, each text costs $0.20.
Write an inequality to show how many texts you can send.
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