what is the value of x in the diagram?

A. 1/2
B. 4/21
C. 2
D. 4
The fractions for cross multiplication are 9/4x-2 and 12/3x+2
I tried to do it but it was not an answer and i dont know what i did wrong

Hard to say what you did wrong, since you didn't show your work.

First, learn to use parentheses:

9/(4x-2) = 12/(3x+2)
9(3x+2) = 12(4x-2)
27x+18 = 48x-24
21x = 42
x = 2

but how did you get to 21x=42 i dont get what you did @Steve

you cross multiply

To get 21x=42, you move the constants to one side and the terms with variables to the other.

27x+18=48x-24
+24 +24
-------------------------------
27x+42=48x
-27x -27x
--------------------------
42=21x

Well, it seems like you got stuck on this math problem. Don't worry, I'm here to help you out with a smile! Let's break it down together.

The fractions you provided are 9/(4x-2) and 12/(3x+2). We can start by cross-multiplying these fractions. So, we multiply 9 by (3x+2) and 12 by (4x-2).

9(3x+2) = 12(4x-2)

Now, let's simplify this equation:

27x + 18 = 48x - 24

To find the value of x, let's bring all the x terms to one side:

27x - 48x = -24 - 18

-21x = -42

To solve for x, we divide both sides of the equation by -21:

x = (-42) / (-21)

Simplifying further:

x = 2

So, the value of x in the diagram is C. 2.

Hope this answer brings a smile to your face! Keep up the great work!

To find the value of x in the diagram, we can set up an equation using the given fractions for cross multiplication.

First, let's set up the equation:

(9/(4x - 2)) = (12/(3x + 2))

To solve this equation, we can use cross-multiplication.

Multiply the numerator of the first fraction (9) by the denominator of the second fraction (3x + 2), and multiply the denominator of the first fraction (4x - 2) by the numerator of the second fraction (12). Set these two products equal to each other.

9(3x + 2) = 12(4x - 2)

Now, let's simplify and solve for x:

27x + 18 = 48x - 24

Subtract 27x from both sides and add 24 to both sides:

18 + 24 = 48x - 27x

42 = 21x

Divide both sides by 21:

42/21 = (21x)/21

2 = x

Therefore, the value of x in the diagram is 2.

So the correct answer is C. 2