(x-5)/-2=(x-1)/-3

2 min read Jun 17, 2024

Solving the Equation: (x-5)/-2 = (x-1)/-3

This article will guide you through the steps of solving the equation (x-5)/-2 = (x-1)/-3. We'll use the principles of algebraic manipulation to isolate the variable 'x' and find its value.

Step 1: Cross Multiplication

To get rid of the fractions, we can cross multiply. This means multiplying the numerator of the left side by the denominator of the right side and vice versa. This gives us:

-3(x-5) = -2(x-1)

Step 2: Expanding the Equation

Next, we distribute the constants on both sides of the equation:

-3x + 15 = -2x + 2

Step 3: Isolating the 'x' Term

To bring all the 'x' terms together, we'll add 2x to both sides:

-3x + 2x + 15 = -2x + 2x + 2

Simplifying, we get:

-x + 15 = 2

Step 4: Isolating 'x'

Finally, to isolate 'x', we'll subtract 15 from both sides:

-x + 15 - 15 = 2 - 15

Simplifying, we get:

-x = -13

Step 5: Solving for 'x'

To get a positive value for 'x', we'll multiply both sides by -1:

(-1)(-x) = (-1)(-13)

This gives us our solution:

x = 13

Therefore, the solution to the equation (x-5)/-2 = (x-1)/-3 is x = 13.