Help with Algebra?

Question

I need help with a fraction problem and I have to show the work but I don't know how:Help? This is suppose to be the first fraction over 4 and the second over 6

5(x+1) = 3(x-2)
_____ _____
4 6

Answer 1

Cross-multiply

6*5(x+1) = 4*3(x-2)
30(x+1) = 12(x-2)
30x + 30 = 12x - 24
18x = -54
x = -3

Answer 2

First eliminate the denominators
The easy way to think of this is to multiply both sides by 6 to eliminate the six on the right, then multiply both sides by 4 to eliminate the 4 orn the left.

5(x + 1)/4 = 3(x-2)/6
multiply both sides by 6
30(x+1)/4 = 3(x-2)
multiply both sides by 4
30(x+1) = 12(x-2)
Now multiply out what you have
30x + 30 = 12x - 24
Add 24 to each side
30x + 54 = 12x
Subtract 30x from each side
54 = 12x - 30x
54 = -18x
Divide both sides by -18
-3 = x

Answer 3

5(x + 1)/4 = 3(x - 2)/6

On the right hand side, the 3 and the 6 reduce to 1/2, thus becoming.

5(x + 1)/4 = (x - 2)/2

Multiply both sides by 4 eliminates all fractions.

5(x + 1) = 2(x - 2)
5x + 5 = 2x - 4

Move 2x to the left hand side; 5 to the right hand side.

5x - 2x = -4 - 5
3x = -9
x = -3

Answer 4

Here's what you would do: multiply both equations to create a common denominator: 5(x+1)/4 Multiply the entire thing by 3 to get 12 as the denominator. 15(3x +3)/12
For the second one multiply by 2. 6(2x-4)/12. Now you can solve the equations and forget about the denominators.
15(3x+3)=6(2x-4)
Distribute- 45x+45=12x-24
Now solve!
33x= -69
x= about 2.1
Hope I helped! :)

Answer 5

5(x+1)/4=3(x-2)/6
6x5(x+1)=3x4(x-2)
30x+30=12x-24
18x=-54
x=-3

Answer 6

5(x+1)=3(x-2)
----------------------

4 6

5x+5=3x-6
6(5x+5)=4(3x-6)
30x+30=12x-24
18x=-54
x=-3