Thread: Help-Inequalities

hey its me again....i have a math problem an my teacher told me that i was supposed to take things to the other side of the sign an then change the sign wel i got really confused in the process so i need a lil help

my problem is 9-6y<2y-7

can someone pls help me understand this type of problem.thxs

Move all the y variables (with coefficients) on left side and move numbers (constants) on right side.

You will get:
-2y-6y<-9-7
-8y<-16 (multiply both sides with -1)
8y>16 (sign < is changed to > when we multiply with -1)
y>2

I assume you want to solve this equality with regards to y.

Isolating the y's on one side, numbers on other side.

Now you need to divide by a number which is smaller than 0. Rules say you need to switch the less-than to larger-than, as you do not know if y is negative or positive.

Double negative makes positive

There you are

hey i have a ? were solving inequalities an i understand a lil how to do it but know there putting frac an stuf in it...so not cool!

heres my problem
3x+2/5>-x-4/5

i dont understand any of this

Originally Posted by pianogurl1250

hey i have a ? were solving inequalities an i understand a lil how to do it but know there putting frac an stuf in it...so not cool!

heres my problem
3x+2/5>-x-4/5

i dont understand any of this

Well, try to solve it. I don't think its good that you don't even try.
Move all x to one side and numbers to other and try to solve it.

Originally Posted by pianogurl1250

hey its me again....i have a math problem an my teacher told me that i was supposed to take things to the other side of the sign an then change the sign wel i got really confused in the process so i need a lil help

my problem is 9-6y<2y-7

can someone pls help me understand this type of problem.thxs

Your teacher is right or correct. In equations or inequalities, when you take things to the other side, you have to change the original signs.

9 -6y = 2y -7
If you want to take the -6y on the leftside to the rightside,
9 = 2y -7 +6y.

It is actually the shortcut for "add 6y to both sides" if you want to remove the -6y from the leftside.
9 -6y = 2y -7
9 -6y +6y = 2y -7 +6y
9 = 2y -7 +6y ------------same as the shortcut, or transposing, above.

Why do you want to take things to the other side?
Because you want to collect or isolate like terms on the same side.
9 -6y < 2y -7
There is -6y on the leftside, and there is +2y on the rightside.
So you either collect all the y-terms, (terms with the variable y), in the left side or all in the rightside.
9 -6y < 2y -7 -------------original
9 -6y -2y < -7 ------------all y-terms in the leftside,
or, 9 < 2y -7 +6y ------------all y-terms in the rightside.
All 3 inequalities mean the same thing, or all 3 are equal.

Why do you want to collect all y-terms in the same side?
Because you want to eventually isolate the y alone by itself. When that happens, then you get the value of y.

So, for this one way of solving the given inequality, we isolate all the y-terms in the left side, etc:
9 -6y < 2y -7
-6y -2y < -7 -9 ---------why -9?
-8y < -16
Now we want to leave the y alone in the leftside. So we divide both sides by (-8).
I assume you know the rule that when you divide both sides of an inequality by a negative thing, you must reverse the sense or direction of the inequality sign. So here, we must reverse the "<" into ">",
y > 2 -------------answer.

What if we isolate all the y-terms in the rightside?
9 -6y < 2y -7
9 +7 < 2y +6y
16 < 8y
We want the y to be alone by itself so divide both sides by 8.
I assume also that you know when dividing both sides by a positive (or non-negative, non-zero) thing, you do not change the sense/direction of the inequality sign.
Hence,
2 < y

Is that the same as y > 2 ?
If you say yes, then you're good.

if i have the problem -8m+3>27 would my answer be >-3 or <-3......pls help

Originally Posted by pianogurl1250

if i have the problem -8m+3>27 would my answer be >-3 or <-3......pls help

Let me complete what I've started re inequalities. After this, I expect that you understand how to do inequalities. You have to practise on some so that you can get the "feel" of it.

Like in equations, you can check by yourself if your answer is correct.
In equations, you just substitute your answer for the unknown in the original equation to see if your answer will make the equation true. If the equation proves true, then your answer is correct. If equation is false, then your answer is wrong.
-8m +3 = 27
-8m = 27 -3 = 24
m = 24 / (-8) = -3
Check,
-8(-3) +3 =? 27
24 +3 =? 27
27 = 27
True, so, m = -3 is correct.

Suppose you mistakenly got m = 3.
-8(3) +3 =? 27
-24 +3 =? 27
-21 = 27
False, so, m=3 is wrong.

In inequalities, the answer is not exact, [inequality....not exact....umm], because the answer is a set of values for the unknown. Meaning, there are more than one value for the unknown that will make the inequality true.
For your inequality here, you want to know if m > -3, or m < -3.

---- (m > -3) means all values of m that are greater than (-3). And (-3) is not included. So, m can be (-2.45), (-1), (1 beobozillion), ....
To see what ">" means re numbers, draw a number line, draw a separator at the number in question, here it is (-3). Any number greater than that is to the right of the separator. (-2.45) is to the right of the separator at (-3). Etc.
Separator can be a vertical line.
So, to check if m > -3 is correct, we choose a number greater than (-3), plug it into the original inequality and see if that chosen number will make the inequality true. Blah, blah, blah....
Say, m = 0 ----------zero is greater than (-3),
-8m +3 > 27
-8(0) +3 >? 27
0 +3 >? 27
3 >? 27
No, so, m > -3 is wrong.

Check m < -3.
(-4) is less than (-3). -----------see the number line with separator.
-8(-4) +3 >? 27
32 +3 >? 27
35 >? 27
Yes, so, m < -3 is correct.
Confused?
Study this more and try to understand it.

--------------
-8m +3 > 27
-8m > 27 -3
-8m > 24
Divide both sides by (-8), reverse the ">" into "<",
m < -3 -----------answer.

Originally Posted by pianogurl1250

if i have the problem -8m+3>27 would my answer be >-3 or <-3......pls help

You subtract 3 from both sides thus,

Now divide by -8 but you should remeber to change the signs because of the negative sign

Originally Posted by pianogurl1250

hey i have a ? were solving inequalities an i understand a lil how to do it but know there putting frac an stuf in it...so not cool!

heres my problem
3x+2/5>-x-4/5

i dont understand any of this

As usual bring to one side and numbers to the other side thus, add to both sides.

Now subtract from both sides. But remember that .
Thus,

Now divide by 4, but remember that to flip the fraction
Thus,

Q.E.D.