[Need help] Math-098 Graphs/Absolute Value

[Plowed]

I missed one of my lectures and have nobody else to ask for help. I have a homework assignment due at the beginning of my next class along with a exam right at the beginning of class. I am stuck on 3 different problems. I'm not asking for somebody to do them for me, but I am asking for an explanation on how to solve them. Feel free to change the problem up so you don't feel like you're just helping me with my homework. Here are the 3 problems I have.

1. Solve the absolute value equation.
|5x+3|=|2x-7|

2. Graph (Shade on true side)
3x-2y >= 6

3. Graph the solution to the system of linear inequalities. (Shade on true side)
2x+3y =< 6
3x-2y =< 6

[Telemanchos]

Since no-one has helped you out yet, I guess I could : )

1. Even though I assume you're famaliar with the | | operator, I'll shortly resume it:
If x is a real number, then | x | = x if x >= 0, | x | = -x if x < 0. So basicly | x | is always positive for any given number. The only thing it does is change the sign of said number if it's negative.

So in your case we'll have 2 equations:
(5x+3)=(2x-7) or (5x+3)=-(2x-7).
All that's left is to solve both equations seperately, which should give you 2 solutions: x = -10/3 or x = 4/7. These 2 are both solutions of your original equation (Test it! ^^)


For your next questions, I'm not in the mood to draw some graphs in paint, so I'll try to explain it without it.

2. When you're asked to graph an inequation, it's best to put it in the standard form.
y =< (3/2 x -3) (Remember to switch the inequation sign around if you multiply both sides with (-1) ! )

Now for the graph, start with the graph for the equation (Which will be a straight line).
y = 3/2 x - 3
The next part might be tricky for you to understand, but you'll see that the line cuts your plane in 2. One of these 2 parts will be the true section, the other one the false one. To verify this you take a random point in one of the sections (Not a point on the line itself ofcourse) and check wether it fullfils the inequation or not, if it does then the section of that point is the true side, if it doesn't it's the false side. Let's say (x,y) = (2,-2), we get -2 =< 3/2*(2) - 3 = 0, since -2 =<0 thi is true. So the section with the point (2,-2) is the true one (that's the one you have to shade). You could also test that the point (1,1) does not fullfil the inequation, which is what we would expect.

3. These are the same as (2), so try yourself ^^


I hope this'll help. I'm currently in my second bachelor year in mathematics, it's been a while since I saw this in highschool, so I've tried to make it as understandable as possible.
Enjoy!

[Plowed]

Okay thank you I get it now. I made it more difficult than it really was. haha
I figured that's how you would do it, but the two absolute values threw me off. Same with the true side/false side.
Once again thanks for taking the time to explain this to me

[Aurust]

This type of thread i believe is against the rules too bad I dont think you can ask questions like straight up answer this question but more along the lines of asking for guidance *shrugs*