Question with inequalities x+4+2x>4x+8?

Question

Ok so the next line would be:
3x+4>4x+8 -Now I change sign
4 -4>x - Is this correct or would I not change it?

Ok so one person says I only change signs when I divide While another said when Ever a negative crosses the = sign so which is it? And If it is only when I divide is it also when I multiply by a negative? And do you change it "every" time a negative crosses or just one time in a problem?

Answer 1

You shouldn't have changed the sign in the first place. You only change the sign when you divide by a negative.

EDIT: Yes, change the sign when you multiply by a negative as well.

If you prefer, you don't EVER have to change the sign. You can just add the negative number to both sides.

So you have 3x + 4 > 4x + 8.
Either subtract 3x from both sides 4>x + 8
or subtract 4x from both sides -x + 4>8

Then you have either -4>x (top one: subtract 8)
or -x > 4 (bottom one: subtract 4)

Now obviously -4>x is the same as x<-4
The bottom one isn't as obvious--you can divide (or multiply) by -1 and switch the sign x<-4
Or you can add x to both sides 0>x + 4
and subtract 4 from both sides -4 >x

See, those are the same thing.

Answer 2

x + 4 + 2x > 4x + 8
Combine like terms (inequality sign never changes when you do this)
3x + 4 > 4x + 8
Subtract 3x from each side (inequality sign never changes when you add or subtract)
4 > x + 8
Subtract 8 from each side (inequality sign never changes when you add or subtract)
-4 > x

Note: The sign ONLY changes when you divide or mulitply by a negative number.
Examples:
5x < 25
Divide both sides by 5
x < 5 (The sign did not change because you divided by a positive number)

-7x < 42
Divide both sides by -7
x > -6 (The sign changes because you divided by a negative number)

You can look at this with real numbers as well.
You know that 2 < 5
Multiply both sides by 10
20 < 50 This is true
Go back to 2 < 5
Multiply both sides by -10
-20 < -50
Now you know that -20 is not less than -50, so you need to switch the sign
-20 > -50

Answer 3

Actually, it is correct. 4-8=-4
You got it right

Answer 4

i dont understand this :(((((((((((((((( i am only ten.is that some kind of high school genius question.or what?