Sure, let's solve the equation step-by-step:
We start with the equation:
[tex]\[
\frac{2x - 1}{5} = \frac{3x - 2}{7}
\][/tex]
Step 1: Eliminate the fractions by finding a common denominator.
In this case, the common denominator for 5 and 7 is 35. So we will multiply both sides of the equation by 35:
[tex]\[
35 \cdot \frac{2x - 1}{5} = 35 \cdot \frac{3x - 2}{7}
\][/tex]
Step 2: Simplify each side.
[tex]\[
7 \cdot (2x - 1) = 5 \cdot (3x - 2)
\][/tex]
Step 3: Distribute the numbers across the parentheses.
[tex]\[
7 \cdot 2x - 7 \cdot 1 = 5 \cdot 3x - 5 \cdot 2
\][/tex]
[tex]\[
14x - 7 = 15x - 10
\][/tex]
Step 4: Collect like terms.
First, we move all terms involving [tex]\( x \)[/tex] to one side and constant terms to the other side. Let's move [tex]\( 14x \)[/tex] to the right side and [tex]\(-10\)[/tex] to the left side by adding 7 to both sides and subtracting [tex]\(14x\)[/tex] from both sides:
[tex]\[
-7 + 10 = 15x - 14x
\][/tex]
Step 5: Simplify the equation.
[tex]\[
3 = x
\][/tex]
So, the solution to the equation is:
[tex]\[
x = 3
\][/tex]
