General Algebra math question?

Question

lets say u have a problem like...

(3x+6)/2 = 5(2x+3)/6

what is the first thing i would do to solve this?

i think i would distribute the 5 to the (2x+3) so 10x+15 it will be.
then i must multiply both sides by the denomenators?
do i need to find a common denominator or just multiply each side by the other denominator? then would multiplying by the denominators cancel the bottom then i need to multipy it by the numerators?im confused.

Answer 1

I think the way you said it is probably best. I would do it the following way:

(3x+6)/2 = 5(2x+3)/6.
(3x+6)/2 = (10x+15)/6. (Distribute the 5)
18x+36 = 20x+30. (Multiply each side by other denominator)
2x = 6. (Move x's and constants to each side)
x = 3.

Hope that helps out.

Answer 2

Okay, first you're right, distribute the 5(2x+3), so you get 10x+15. Now you have:
(3x+6)/2 = (10x+15)/6
Then you much find a common denominator (6)... so multiply the first part of the problem by 3/3, and you get:
3(3x+6)/6 = (10x+15)/6, distribute the 3(3x+6) and you get:
(9x+18)/6 = (10x+15)/6
Now multiply each side by 6 to get rid of it, and you get
9x+18 = 10x+15
Subtract 15 from both sides:
9x+3 = 10x
Subtract 9x from both sides:
3=x
the answer is x=3
If you want you can check to see if x=3 is true for this problem.

Answer 3

You are on the right track.

Yes, first distribute the 5:

(3x+6)/2 = (10x+15)/6

Next, you can simply cross multiply:

2*(10x+15) = 6*(3x+6)

Distribute:

20x + 30 = 18x + 36

Combine like terms:

2x = 6

x = 3.

NOTE: Whenever you have a problem such as this (a fraction = a fraction) you can always cross multiply, keeping the equations equal to one another. Cross multiplying is the same thing as finding a common denominator, but it eliminates allot of extra steps!

Answer 4

(3x + 6) / 2 = 5(2x + 3) / 6

The distributive property on the right side of the equation

(3x + 6) / 2 = (10x + 15) / 6

Solve as a proportional problem

The means is 2((10x + 15)

The extremes is 6 (3x + 6)

The equation

2(10x + 15) = 6(3x + 6)

The distributive property on the left and right side of the equation.

20x + 30 = 18x + 36

Transpose 18x

20x + 30 - 18x = 18x + 36 - 18x

Collect like terms

2x + 30 = 36

Transpose 30

2x + 30 - 30 = 36 - 30

Collectg like terms

2x = 6

Divide both sides of the equation by 2

2x / 2 = 6 / 2

x = 6/2

x = 3

- - - - - - - -s-

Answer 5

U CANOT FIND COMMON DENOMINATORS.. its an equal sign there not an operation...

u work it like so:


(3xt6)/2 = 5(2xt3)/6
what u do on one side u have to do on the other side. so u have to remove the denominators. to do this u have to multiply the left side (the whole side) by 6 and the whole right side by 2. its like you are criss crossing the numbers and instead of divide as it was before u multiply.

it will look like this now

6(3x+6) = 2*5(2x+3)

u simplify to

6(3x+6) = 10(2x+3)
18x + 36 = 20x + 30
bring like polynomials to one side:
36 - 30 = 20x -18x
of course when u go across the equal sign the sign changes from plus to minus and vice versa

6 = 2x
x = 3

thats the answer. that how i do it here in jamaica anyway. dunno if u americans have a different method

Answer 6

I would cross multiply first. That way, you don't need to distribute more than you have to.
(3x+6)/2 = 5(2x+3)/6

6(3x+6) = 10(2x+3)

Now distribute and solve for x.
18x+36 = 20x + 30
2x = 6
x =3

Answer 7

X by 6:-
3(3x + 6) = 5(2x + 3)
9x + 18 = 10x + 15
3 = x

Answer 8

10(2x+3)=6(3x+6)
20x+30=18x+36
2x=6
x=3

Answer 9

you need to find a common denominator

then eliminate the denominators.