Math Problem Statement

Solve the equation 1/(2x - 3) = 3/(4x + 2).

Solution

The equation in the image is:

12x3=34x+2\frac{1}{2x - 3} = \frac{3}{4x + 2}

To solve for xx, follow these steps:

  1. Cross-multiply to eliminate the fractions:

1(4x+2)=3(2x3)1 \cdot (4x + 2) = 3 \cdot (2x - 3)

  1. Distribute on both sides:

4x+2=6x94x + 2 = 6x - 9

  1. Move all terms involving xx to one side and constant terms to the other:

4x6x=924x - 6x = -9 - 2

  1. Simplify the equation:

2x=11-2x = -11

  1. Solve for xx:

x=112=112=5.5x = \frac{-11}{-2} = \frac{11}{2} = 5.5

So, the solution is x=5.5x = 5.5.

Would you like further details, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. How would the solution change if the equation were 12x3=24x+2\frac{1}{2x - 3} = \frac{2}{4x + 2}?
  2. Can you solve a similar equation with different coefficients, such as 23x1=45x+7\frac{2}{3x - 1} = \frac{4}{5x + 7}?
  3. What happens if both sides of the equation have additional constants, like 1+32x3=3+14x+2\frac{1 + 3}{2x - 3} = \frac{3 + 1}{4x + 2}?
  4. How would you solve an equation where the denominators involve quadratic expressions, like 1x24=3x2+2x\frac{1}{x^2 - 4} = \frac{3}{x^2 + 2x}?
  5. What is the geometric interpretation of the equation 12x3=34x+2\frac{1}{2x - 3} = \frac{3}{4x + 2}?

Tip: When solving equations involving fractions, cross-multiplication is a powerful tool to eliminate the fractions and simplify the equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Cross-multiplication

Theorems

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Suitable Grade Level

Grades 9-10