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(m-3)/2-(2m+1)/3+m/5+3=2m-1/3

2 min read Jun 16, 2024
(m-3)/2-(2m+1)/3+m/5+3=2m-1/3

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

This article will guide you through the steps of solving the equation (m-3)/2-(2m+1)/3+m/5+3=2m-1/3.

Step 1: Find a Common Denominator

The first step is to find a common denominator for all the fractions in the equation. The least common multiple of 2, 3, and 5 is 30.

  • Multiply the first fraction by 15/15: (m-3)/2 * (15/15) = (15m-45)/30
  • Multiply the second fraction by 10/10: (2m+1)/3 * (10/10) = (20m+10)/30
  • Multiply the third fraction by 6/6: m/5 * (6/6) = (6m)/30

Now the equation looks like this:

(15m-45)/30 - (20m+10)/30 + (6m)/30 + 3 = (2m-1)/3

Step 2: Simplify the Equation

  • Combine the fractions on the left side of the equation: (15m - 45 - 20m - 10 + 6m)/30 + 3 = (2m-1)/3
  • Simplify the numerator: (m-55)/30 + 3 = (2m-1)/3

Step 3: Eliminate Fractions

  • Multiply both sides of the equation by 30: (m-55) + 90 = 10(2m-1)
  • Distribute on the right side: (m-55) + 90 = 20m - 10

Step 4: Isolate the Variable

  • Subtract m from both sides: -55 + 90 = 19m - 10
  • Add 10 to both sides: 35 = 19m
  • Divide both sides by 19: m = 35/19

Solution

The solution to the equation is m = 35/19.

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