Let's solve the given equation step by step:
The given equation is:
[tex]\[
\frac{x-1}{5} = \frac{x-1}{2}
\][/tex]
### Step 1: Eliminate the denominators
To get rid of the fractions, we can cross-multiply. This means we multiply both sides of the equation by the denominators:
[tex]\[
2 \cdot (x-1) = 5 \cdot (x-1)
\][/tex]
### Step 2: Distribute the terms
Next, we expand both sides by distributing the constants inside the parentheses:
[tex]\[
2x - 2 = 5x - 5
\][/tex]
### Step 3: Move all terms involving [tex]\( x \)[/tex] to one side
To isolate [tex]\( x \)[/tex], we need to get all terms involving [tex]\( x \)[/tex] on one side and constant terms on the other side. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[
2x - 2 - 2x = 5x - 5 - 2x
\][/tex]
This simplifies to:
[tex]\[
-2 = 3x - 5
\][/tex]
### Step 4: Solve for [tex]\( x \)[/tex]
Now, isolate [tex]\( x \)[/tex] by moving the constant term to the other side. Add 5 to both sides:
[tex]\[
-2 + 5 = 3x - 5 + 5
\][/tex]
This simplifies to:
[tex]\[
3 = 3x
\][/tex]
Finally, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{3}{3} = 1
\][/tex]
So, the solution to the equation is:
[tex]\[
x = 1
\][/tex]
