To solve the proportion [tex]\(\frac{3x - 3}{4} = \frac{2x + 1}{3}\)[/tex] using cross multiplication, follow these steps:
1. Set up the cross multiplication:
Multiply the numerator of the left fraction by the denominator of the right fraction and the numerator of the right fraction by the denominator of the left fraction:
[tex]\[
3 \cdot (3x - 3) = 4 \cdot (2x + 1)
\][/tex]
2. Distribute the constants:
Expand both sides of the equation:
[tex]\[
3 \cdot (3x - 3) = 3 \cdot 3x - 3 \cdot 3 = 9x - 9
\][/tex]
[tex]\[
4 \cdot (2x + 1) = 4 \cdot 2x + 4 \cdot 1 = 8x + 4
\][/tex]
So, the equation becomes:
[tex]\[
9x - 9 = 8x + 4
\][/tex]
3. Isolate the variable:
First, let's move all the [tex]\(x\)[/tex] terms to one side of the equation and the constants to the other side. Subtract [tex]\(8x\)[/tex] from both sides:
[tex]\[
9x - 8x - 9 = 4
\][/tex]
Simplifying this gives:
[tex]\[
x - 9 = 4
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add 9 to both sides of the equation:
[tex]\[
x - 9 + 9 = 4 + 9
\][/tex]
Simplifying this gives:
[tex]\[
x = 13
\][/tex]
Thus, the solution to the equation [tex]\(\frac{3x - 3}{4} = \frac{2x + 1}{3}\)[/tex] is [tex]\(\boxed{13}\)[/tex].
