Help! I am stuck on my maths homework! Can you solve this inequality step by step and show me how it works?

Question

4-6x<22!

Answer 1

4-6x<22
-4 -4
-6x<18
-6/ -6/
x> -3
when you divide by a negative you have to switch the sign

Answer 2

x > –3

When you see this kind of problem on a test, it usually is there to see if you remember to reverse the inequality sign when you have a step involving multiplication or division with a negative number. So be on the look-out for such a step. Actually, most math testing questions have a hallmark to look for, like this one, so an aid to doing well on tests is to learn those as well as the techniques themselves.

However, if you don't register this "trick" well and inequality questions hammer your scores, then do them like this:

4 – 6x < 22
4 – 6x + 6x < 22 + 6x
4 < 22 + 6x
4 – 22 < 22 + 6x – 22
–18 < 6x
–18/6 < 6x/6
–3 < x

and you never have to do that step at all. And if you feel you simply have to state the answer with "x" first, it is obvious and easy to see that "–3 < x" means "x > –3" so even though you use the technique to polish your answer, you aren't really aware of it, you are simply using clear logic.

Finally, to "Bill" and his lame crack from "Benchwarmers" — "maths" is quite correct. And so "Englishes" would be showing ignorance, not showing ignorance up. If you know your Englishes Bill, you know there's a difference there...

Answer 3

Sure....

4 - 6x < 22 Subtract 4 from each side....
-6x < 22 - 4
-6x < 18

Now you need to divide both sides by -6. When you multiply or divide both sides of an inequality by a negative number, you need to flip the sign. So....

x > -3

Check your answer in the original...
If your answer is x> -3 , then that means that any number greater than -3 should work in the equation. I'll pick 0 because it's easy to check.
4 - 6(0) < 22
4 - 0 <22
4 < 22

Since 4 is less than 22, then we know that our answer is right.

Answer 4

Inequalities are solved for x the same as equalities. The only trick is if dividing by a negative number, where you must flip the sign.

4-6x<22
-6x<18
x>-3

Answer 5

-6x<22-4

-6x<18

divide both sides by -6, since you're dividing by negative number change inequality sign

(-6/-6)x> 18/(-6)

x>-3


how it works?

take number greater than -3 and your inequality should be true
let's take 2
4- 6*2<22
-8<22
this is obviously true

take number less then -3, let's say -5

4-6(-5)<22

34<22
this is false

Answer 6

-6x < 22-4
-6x <18 than divide both sites by -1 and turn sign around
6x > -18
x > -3

Answer 7

-6x < 22-4
-6x < 18
-6x/6 < 18/6
-x < 18/6
-x < 3
-x/-1 < 3/-!
=x > -3

Answer 8

4-6x<22

Subtract 4 from both sides

4-4-6x<22-4
-6x<18

Now add 6x to both sides

6x-6x<18+6x
0<18+6x

Now subtract 18 from both sides

0-18<18-18+6x
-18<6x

Now divide both sides by 6

-18/6<6x/6
-3
which is the same as x>-3

Answer 9

In this problem, you'd sove it just like you would 4-6x=22
so it would be
4-6x<22
-6x<18
but then because you are diving by a negative you have to swite the less than sign to greater than
x>-3

Answer 10

4-6x<22 is 4-6 times4 which is 4-24 which would be 20! making it less than 22! 4-24=20 the < means less than! that is my best guess. i barely passed an algerba class