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(2x-3)/6=2x/3+1/2

2 min read Jun 16, 2024
(2x-3)/6=2x/3+1/2

Solving the Equation: (2x-3)/6 = 2x/3 + 1/2

This article will guide you through solving the equation (2x-3)/6 = 2x/3 + 1/2 step-by-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 6, 3, and 2 is 6.

  • Multiply the second term (2x/3) by 2/2: (2x/3) * (2/2) = 4x/6
  • Multiply the third term (1/2) by 3/3: (1/2) * (3/3) = 3/6

The equation now becomes: (2x-3)/6 = 4x/6 + 3/6

2. Simplify the Equation

Since all fractions have the same denominator, we can eliminate them and work with the numerators only:

(2x - 3) = 4x + 3

3. Solve for x

  • Combine like terms: Subtract 2x from both sides and subtract 3 from both sides:

    • (2x - 2x - 3) = (4x - 2x + 3 - 3)
    • -3 = 2x

  • Isolate x: Divide both sides by 2:

    • -3 / 2 = 2x / 2
    • -3/2 = x

Solution

Therefore, the solution to the equation (2x-3)/6 = 2x/3 + 1/2 is x = -3/2.

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