Math Equations?

Question

1.) Solve for "x":
2x + 1
_____
6
=
x + 3
____
2


2.) Solve for "x":
x + 2
____ -(minus)
2

x
_ =
3

x - 3
____
4
Please show your work, thank you.

Answer 1

1]
We have
(2x+1)/6 = (x+3)/2

You know (ofcourse) that division on one side of the equal sign is mulitplication on the other side:

(2x +1) 2 = (x + 3) 6

We have to expand this:

4x + 2 = 6x + 18

addition is subtration on the other side:

4x - 6x = 18-2
- 2x = 16
x = 16/-2 = -8. (deviding by positive number by a negative number gives a negative number.)
check by filling x=-8 in.

2]
(x+2)/2 - x/3 = (x-3)/4
We don't like those dividing numbers, do we? Multiply by 2 and mult. by 3 and mult by 4 to get rid of them. It will work: Multiply every term in the equaiton by 2*3*4 = 24

(x+2)/2 * 24 - x/3 * 24 = (x-3)/4 * 24
(x+2) 12 - x 8 = (x-3) 6
(expand)
12x + 24 - 8x = 6x - 18 (brings x's together)
-2x = -42
x = 21. (negative /negative = positive)

Answer 2

It is difficult to tell from the format of your question what equations you are solving. But this may help you find your answers:

I think you have equations where one fraction is equal to another fraction, and there are complex algebraic terms in some of the numerators and denominators. The following formula always works for solving two fractions which are equal:

(a/b) = (c/d) can be expressed as (a x d) = (c x b)
(This is a shortcut. The long way is to multiply both sides of the equation by the same value. You would have to do it two times, once for b and again for d. Memorizing the formula makes it faster.)

If you have a piece of scratch paper, the easy way to do this is to set all the numerator terms over a very long fraction bar and put all the denominator terms below. Do this for the left and the right side of the equation. Then, think of the equation like an "X", and multiply the numerator and denominator expressions connected by the lines of the "X". This gives you the
"a times d equals c times b"
(Remembering this "X" layout will help you answer test questions faster, and reduce mistakes.)
Then do normal algebra to simplify both sides of the equation and solve for x.

Answer 3

1.) x= -10/36
i dont have a scanner theres no way i can show u my work..? sry. but i can explain it to u if u'd like?