Word problems and solving for inequalities

[Soup]

Alrighty, so I have a math test coming up and I'm trying to figure out these problems my teacher gave me in the review packet. She also gave us the copy of the key, so I have the answers but I'm confused at how she got those answers.

Word Problem:

Kiran drove from Tortula to Cactus, a distance of 250 miles. She increased her speed by 10mi/h for the 360-mile trip from Cactus to Dry Junction. If the total trip took 11 hours, what was her speed from Tortula to Cactus?

So far this is what I figured out.

From Tortula to Cactus
Distance = 250 miles
Rate = x mph
Time - yh

From Cactus to Dry Junction
Distance = 360 miles
Rate = x+10 mph
Time = 11-yh

That's where I stopped because I'm not sure how to put that into a problem I can solve.

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Solving Inequalities

I have no idea how to put in math symbols in these topics so I just decided to write it out on the computer. Here are the problems

Problem 1

Whats stumping me on this one is the second step that my teacher did. How did it turn into a -9?

Problem 2

Sorry about this. I know I'm supposed to show my work, but the problem is I had no work D: This was the work and answer that was on the answer key. I don't know where to start first and I have no idea what that graph is supposed to show. What exactly is that table anyway and what do I use for it?

Problem 3

Um... yeah. I followed her up to the part where she subtracted the 1. Then I have no idea where the - came from and why it's there. Also I'm a bit confused with the answer (-infinity,-4]U[2,infinity) How do I determine what number goes where? Oh and I didn't label it but the bottom one is the answer from the key. But I'm pretty sure you guys would have figured it anyway.

Problem 4

Erm. Yeah. I don't even know where I was going with this. Am I supposed to be setting this answer to 0? Is that what I should do first? And again with the answer (-infinity,-9]U[7,infinity) How did she get that and how do you know where to put what number?

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This is for Pre-Calc by the way. That's all of the questions that I'm trying to figure out. I hope I didn't make anything too confusing. Any help would be very much appreciated.

 

[fasteddie65]

Alrighty, so I have a math test coming up and I'm trying to figure out these problems my teacher gave me in the review packet. She also gave us the copy of the key, so I have the answers but I'm confused at how she got those answers.

Word Problem:

Kiran drove from Tortula to Cactus, a distance of 250 miles. She increased her speed by 10mi/h for the 360-mile trip from Cactus to Dry Junction. If the total trip took 11 hours, what was her speed from Tortula to Cactus?

So far this is what I figured out.

From Tortula to Cactus
Distance = 250 miles
Rate = x mph
Time - yh

From Cactus to Dry Junction
Distance = 360 miles
Rate = x+10 mph
Time = 11-yh

That's where I stopped because I'm not sure how to put that into a problem I can solve.

Since d = rt, t = d/r

250/x + 360/(x + 10) = 11
Multiply by the least common denominator: x(x + 10)

250(x + 10) + 360x = 11x(x + 10)
250x + 1500 + 360x = 11x^2 + 110x

I let you finish it.


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[fasteddie65]

Problem 1: 6 - x ? 2x + 9
+ x + x

6 ? 3x + 9
-9 - 9

-3 ? 3x

-3/3 ? 3x/3

-1 ? x

 

[fasteddie65]

Problem 2:

The chart is called a sign graph. You look at the signs (+ or -) of the factors or terms of the inequality, and determine whether each side is positive or negative.

The inequality (3 + x)/(3 - x) ? 1 becomes (3 + x)/(3 - x) - 1 ? 0

Combining the two terms into one: (3 + x)/(3 - x) - (3 - x)/(3 - x) ? 0

2x/(3 - x) ? 0

You look at the signs of 2x and 3 -x over various intervals, and then the sign of the rational expression.

When the expression is positive, you have solved the original inequality.