algebra b help please??????????

Question

how do you solve for x?? 2/3(x+1)=5/6(x+2)

please

Answer 1

Are the x +1 and x + 2 in the denominator? If so, then proceed as follows:

The easiest way to do this type of equation (a fraction = a fraction) is to cross multiply. That means multiply the denominator of the right (left) side times the numerator of the left (right) side and set them equal to each other. So in your problem, multiply 3(x + 1) times 5 and multiply 6(x + 2) times 2. This will give you

2*6(x + 2) = 5*3(x + 1)
12(x + 2) = 15(x + 1)
12x + 24 = 15x + 15

Now add -12x to both sides and you get

24 = 3x + 15.

Now add -15 to both sides and you get

9 = 3x

Divide both sides by 3 and you get

x = 3.

Check: 2/3(3 + 1) ?= 5/6(3 + 2)
2/12 ?= 5/30
1/6 = 1/6

If the x + 1 and x + 2 are NOT in the denominators then cross multiply by multiplying 3 times 5(x + 2) and 6 time 2(x + 1). This will give you

3*5(x + 2) = 6*2(x + 1)
15(x + 2) = 12(x + 1)
15x + 30 = 12x + 12
3x + 30 = 12
3x = -18
x = - 6

If the x + 1 and x + 2 are in the denominators, then the problem should have been typed

2/[3(x + 1)] = 5/[6(x + 2)]

The way the problem was typed originally, the x + 1 and
x + 2 are in the numerators.

Answer 2

First, distribute the fractions over the parenthesis:

2/3x+2/3=5/6x+10/6

Find the lowest common denominator and convert everything to sixths:

4/6x+4/6=5/6x+10/6

Move x's to the left and others to the right:

-1=1/6x

Divide both sides by 1/6:

-6=x.

(I think)

Answer 3

Multipy both sides by 6
4(x+1)=5(x+2)

Multipy brackets
4x+4 = 5x+10

Subtract 10 from both sides
4x-6 = 5x

subtract 4x from both sides
-6 = x