Math Problem Statement

Solve the equation: (x - 3) / (2x + 5) - 6x / (3x - 4) - 8 / (4 - 3x) = 1 1/2

Solution

The equation from the image is:

x32x+56x3x4843x=112\frac{x - 3}{2x + 5} - \frac{6x}{3x - 4} - \frac{8}{4 - 3x} = 1 \frac{1}{2}

First, let's convert 1121 \frac{1}{2} into an improper fraction:

112=321 \frac{1}{2} = \frac{3}{2}

Now, we can solve the equation step by step. Let me calculate the solution.The solution to the equation is approximately:

x3.42x \approx -3.42

Would you like a detailed step-by-step breakdown of the solution process or have any questions?

Here are five related questions to consider:

  1. How do you solve rational equations with multiple fractions?
  2. What are the steps to combine and simplify fractions in algebraic equations?
  3. How can you check if the solution to an equation is correct?
  4. What happens if an equation has no solution or an extraneous solution?
  5. How do you handle complex fractions with variable denominators?

Tip: Always check the domain of the equation to ensure that the denominators do not equal zero for the given solution!

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Math Problem Analysis

Mathematical Concepts

Rational Equations
Algebraic Fractions

Formulas

Convert mixed numbers to improper fractions: a b/c = (ac + b)/c
Simplification of rational expressions
Finding common denominators to subtract fractions

Theorems

Cross-multiplication for solving rational equations
Properties of equality

Suitable Grade Level

Grades 10-12