Question

2x + 5/2 > 3/2x -2 SOLVE FOR X

Answer 1

would I add negative 2 to both sides? or make it a fraction too?

Answer 2

That's one way to do it. If your plan is to eventually isolate the x on the right side.
If you wanted to isolate the x on the left side you would subtract 5/2 from both sides.

Answer 3

How would I solve and get what number X is supposed to be?

Answer 4

sorry actually you want to add 2 to both sides not -2
First step
2x + 5/2 +2 > 3/2x -2 +2
2x + 9/2 > 3/2x

Answer 5

Do you have an idea for what to do next?

Answer 6

Our goal is to isolate the x on the right side, so we need all the x's on the right. How can I move that 2x over to the right?

Answer 7

I would normally say combine like terms lol

Answer 8

Yes, we want to move that 2x over to the right and combine it with the 3/2x. To move it we need to subtract 2x from both sides.

Answer 9

but how would you do it with the fraction? BC idk how you got the 9/2

Answer 10

5/2 + 2 = 5/2 + 4/2 = 9/2

Answer 11

common denominator? is that how you got it?

Answer 12

yes.

Answer 13

Can you write the next step after
2x + 9/2 > 3/2x

Answer 14

9/2 > 7/2x ???

Answer 15

So X would equal 7/2?

Answer 16

Subtract 2x from both sides
2x + 9/2 -2x > 3/2x - 2x
9/2 > 3/2x - 4/2x
9/2 > -1/2x
Your left side is good. Your right side is wrong

Answer 17

I added the 2x

Answer 18

Now, we just have to get rid of that -1/2 to isolate the x. How do we get rid of that -1/2?

Answer 19

flip it?

Answer 20

I don't know.

Answer 21

flip it and multiply by the flipped fraction on both sides. yes

Answer 22

so -1/2 times -2/1?

Answer 23

yes. that just equals 1.

Answer 24

so x is 1?

Answer 25

9/2 (-2/1) > -1/2x (-2/1)
-18/2 > x
-9 > x
or x < -9
x is less than - 9
on inequalities you get x is < or > something . you don't get x = something

Answer 26

I am so confused then

Answer 27

general strategy.
get all your x terms on one side and your numbers without x's on the other
combine like terms.
multiply both sides by the flipped version of your x coefficent

Answer 28

You're confused by what I did in the last few steps?

Answer 29

bc it says solve for x, I thought I was supposed to get a number for x

Answer 30

SO 9/2 > X WOULD BE THE CORRECT ANSWER?

Answer 31

you did solve for x. with inequalities x does not equal just one number though. x can be any number less than -9. Pick any number less than -9 and your original inequality, 2x + 5/2 > 3/2x -2 will be true.

Answer 32

No, the answer is x < -9

Answer 33

see, idk how you flipped it and got just the -9

Answer 34

ooook, I saw your post just now, I didn't see it earlier about flipping it

Answer 35

you have to do the same thing to both sides in algebra. golden rule there.
I had to multiply the right side by -2/1 also. go back up and look. I multiplied 9/2 by -2/1
multiply numerators and denominators to get -18/2 which simplifies to -9/1 or -9

Answer 36

I have one last problem.

Answer 37

uhoh

Answer 38

-3 ( x+1) - x/2 + 3/2 < 0

Answer 39

I distribute the -3 to whats in the ( ) right?

Answer 40

yes

Answer 41

so far I have -3x -3 - x/2 + 3/2 < 0

Answer 42

yes. now combine those x terms (that x/2 is the same as (1/2)x) and combine the -3 and +3/2

Answer 43

would that be - 4x/2?

Answer 44

bc I found the common denominators

Answer 45

no. -3x - (1/2)x = -6/2x - (1/2)x = (-7/2)x

Answer 46

ok, I see where I went wrong.

Answer 47

so the next thing would be to add -3 to 3/2 and I got 3/2 for the answer?

Answer 48

no. -3 + 3/2 = -6/2 + 3/2 = -3/2
that minus sign is important

Answer 49

So I have the 3/2 right, just not the negative right?

Answer 50

yes. so what do we have now?
(-7/2)x - 3/2 < 0
what's next?

Answer 51

adding the -3/2 to both sides?

Answer 52

add 3/2 to both sides

Answer 53

so I was right?

Answer 54

except for the -...yes

Answer 55

(-7/2)x - 3/2 + 3/2 < 0 + 3/2
(-7/2)x < 3/2
Now multiply both sides by -2/7 to get
x < 3/2 (-2/7)
x < -6/14
x < -3/7
sorry gotta run. good luck!

Answer 56

thank you