how do you work out x+5>3x-4?

Add 4 to both sides then you have
x+9 >3x

Then subtract an x from both sides, you have
9 > 2x

Divide both side by 2 and you have
4.5 > x or x < 4.5

square both sides and then solve as a quadratic the 2 answers will be your limits.
I'm sure you can do that yourself

3x-4<x+5
3x-x<5+4
2x<9
x<4.5

9>2x
9/2>x

9 > 2x
x < 9/2

x + 5 > 3x - 4
x - 3x > -5 - 4
-2x > -9
x < -9/-2
x < 9/2 (4.5)

What I used to do to solve these was to look at the greater than / less than symbol as an equal sign, and then solve. After I solved, I replaced equal with the correct sign.

Hope this helps!!!

x+5 > 3x-4
subtract x from both sides
5 > 2x - 4
add 4
9 > 2x
9/2 > x

Add 4 to each side to get:
x+9>3x

Subtract x from each side to get:
9<2x

Divide each side by 2 to get:
4.5<x

you need to put 'x's on one side and numbers on the other.
so:
x+5>3x-4
x-3x>-4-5
-2x>-9
-x>-4.5
x<4.5

thats step by step so you will see how its done