Big Math Help?

Question

1.solve the inequality -4y+6<-14
2.solve the inequality7+x<_10
3.In how many ways can you arrange 8 books on a shelf?

Answer 1

1. Subtract 6 from each side =>-4y<-20 => y>5 (dividing by negative number reverses inequality)

2. x<=3 Just subtract 7 from each side.

3. 8!=8x7x6x5x4x3x2x1 You do the math.

Answer 2

You will have to do your own work, but I will show you some examples:

Solve 2t+5>7 the idea is to get the variable alone on one side of the inequality. Here I can subtract 5 from either side and then divide both sides by 2:
2t+5>7
2t+5-5>7-5
2t>2 now divide both sides by 2
t>2

There is a trick if you have to multiply or divide by a negative. You have to "reverse" the inequality.
7-5s<-8 subtract 7 from both sides
7-7-5s<-8-7
-5s<-15 now divide by -5, don't forget to change the inequality
s>3

We could also do this:
7-7-5s<-8-7
-5s<-15 add 5s to both sides
-5s+5s<-15+5s
0<-15+5s now add 15 to both sides
0+15<-15+15+5s
15<5s divide both sides by 5
3
If 3 is less than s, then s is greater than 3 which was the first answer.

For the last question let's assume that order matters. That is if we had two books A and B, then AB would be different from BA. Now you have to ask yourself "How many choices are there for the first book?" Well there are 8. If we were only placing 1 book there would be 8 choices. So how many choices are there for the second book (remember we already used one book)? There are 7 since there are seven books left. Now each of our first 8 choices has 7 choices to go with it. So we have 8x7=56 choices for arranging 2 of the 8 books. Follow on through for the remaining choices.

Answer 3

-4y+6<-14
subtract 6 from both sides
-4y<-20
divide by -4 (switch direction of the sign w/ negatives)
y>5

7+x<=10
subtract 7 from each side
x<=3

Of course you can arrange books vertically, horizontally, somewhere in between, it would depend on the shelf space, # shelves, etc.

However your problem probably assumes there are only 8 total locations for these books....

You can put the 1st book in any of 8 positions, then the 2nd in any of remaining 7, etc..

8! = 8*7*6*5*4*3*2*1=40320

Answer 4

1. -4y>-14-6
-y>-20/-4
y>-5 (don't forget to flip the > or the < in these types of problems)

2. x<_3 (don't flip this one because it also has an = sign)

3. 8x7x6x5x4x3x2x1 = Get a calculator

Answer 5

1. -4y<-20 -6 to both sides
y<5 divided by -4 on both sides

2. x<-17 -7 to both sides

3. 8*7*6*5*4*3*2*1 which is 40320

Answer 6

3 is 36

Answer 7

1. y>5
2. x<_3

Answer 8

1.y<5
2.x<-17
3.64