Certainly! Let's solve the equation step-by-step using cross multiplication.
Given the equation:
[tex]\[
\frac{3x - 3}{5} = \frac{2x - 2}{4}
\][/tex]
Step 1: Cross-multiply both sides to eliminate the fractions.
This means we multiply the numerator on the left by the denominator on the right, and the numerator on the right by the denominator on the left:
[tex]\[
4 \cdot (3x - 3) = 5 \cdot (2x - 2)
\][/tex]
Step 2: Distribute the numbers on both sides of the equation:
[tex]\[
4 \cdot 3x - 4 \cdot 3 = 5 \cdot 2x - 5 \cdot 2
\][/tex]
[tex]\[
12x - 12 = 10x - 10
\][/tex]
Step 3: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side. We start by subtracting [tex]\( 10x \)[/tex] from both sides:
[tex]\[
12x - 10x - 12 = 10x - 10x - 10
\][/tex]
[tex]\[
2x - 12 = -10
\][/tex]
Step 4: Add 12 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x - 12 + 12 = -10 + 12
\][/tex]
[tex]\[
2x = 2
\][/tex]
Step 5: Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{2}{2}
\][/tex]
[tex]\[
x = 1
\][/tex]
Thus, the solution to the equation is:
[tex]\[
x = 1
\][/tex]
