algebra help plz?

Question

3(x-2)/4 + 2x-3/8 - 1-2x/3 =2
the answer is: 101/40

The problem: I know you have to times each part by a common demoninator which is 24 but im just stuck on multiplying 24 by 3(x-2)/4 which is the first part of the equation.

Question: Should i expand 3(x-2)/4 first then times 24?

Answer 1

3(x-2)/4 + 2x-3/8 +1-2x/3 =2
Simplify the first numerator using the distributive property.
3x-6/4 + 2x-3/8+ 1-2x/3 =2

You have already determined that 24 is the common denominator, so multiply each side by 24.

The 4 will cancel out leaving 6, the 8 will cancel out leaving 3, and the 3 will cancel out leaving 8. So, the equation becomes:

6(3x-6) + 3(2x-3) - 8(1-2x) = 48
18x-36+6x-9-8+16x=48
Combine like terms:
40x-53=48
Add 53 to each side:
40x=101
Divide by 40:
x=101/40

Answer 2

Question: Should i expand 3(x-2)/4 first then times 24?
Your choice.The same as asking if i want to eat the frenchfries or hamburger first.Do whatever you think it is easier for you.

3(x-2)/4 + (2x-3)/8 - (1-2x)/3 =2
18(x-2)+6x-9 -8 +16x=48 (Multiply by 24)
18x-36+6x-17+16x=48
40x-53=48
40x=101
x=101/40

Answer 3

just notice
24*3(x-2)/4=4*6*3(x-2)/4

and here we multiply and divide by 4 at the same time; so we can cancel out to obtain

6*3(x-2)=18(x-2)=18x-36.

I hate math.

Answer 4

multiply right and left side by 24


3 (x-2)/4 = 3x-6/4 = 6(3x-6)/24 = 18x-36/24

2x = 48x/24

-3/8 = -9/24

-1 =-24/24

-2x/3 = -16x/24

Sorry i found x = 117/50

Answer 5

No, you don't. All you need to do is multiply 24 times 3(x-2)/4 which leaves you with 6 times 3 times (x-2) which is 18 times (x-2), simplify: 18x-36.

Answer 6

3(x-2)/4 + 2x-3/8 - 1-2x/3 =2

4*6 = 24
8*3 = 24
3*8 = 24

6*3(x-2)/24 + 3*(2x-3)/24 - 8*(1-2x)/24 = 2

6*3(x-2)/24 + 3*(2x-3)/24 - 8*(1-2x)/24 = 2 ||*24
6*3(x-2) + 3*(2x-3) - 8*(1-2x) = 48
18(x-2) + 3(2x-3) - 8(1-2x) = 48
18x - 36 + 6x - 9 - 8 + 16x = 48
40x - 53 = 48 ||+53
40x = 101 ||/40
x = 101/40