Math Problem Statement

2x-3 4x-2 6x-2 ------ + -------- - 2 = -------- 9 7 4

Solution

Let's solve the equation:

2x39+4x272=6x24\frac{2x - 3}{9} + \frac{4x - 2}{7} - 2 = \frac{6x - 2}{4}

Step 1: Clear the fractions

To eliminate the fractions, find the least common multiple (LCM) of the denominators: 9, 7, and 4. The LCM of 9, 7, and 4 is 252. Multiply every term by 252 to clear the fractions:

252×(2x39)+252×(4x27)252×2=252×(6x24)252 \times \left(\frac{2x - 3}{9}\right) + 252 \times \left(\frac{4x - 2}{7}\right) - 252 \times 2 = 252 \times \left(\frac{6x - 2}{4}\right)

Step 2: Simplify each term

28×(2x3)+36×(4x2)504=63×(6x2)28 \times (2x - 3) + 36 \times (4x - 2) - 504 = 63 \times (6x - 2)

Step 3: Distribute and simplify

56x84+144x72504=378x12656x - 84 + 144x - 72 - 504 = 378x - 126

Combine like terms on the left side:

200x660=378x126200x - 660 = 378x - 126

Step 4: Isolate xx

Move all terms involving xx to one side of the equation and constant terms to the other side:

200x378x=126+660200x - 378x = -126 + 660

178x=534-178x = 534

Step 5: Solve for xx

x=534178x = \frac{534}{-178}

Simplify the fraction:

x=3x = -3

The solution is x=3x = -3.

Would you like a detailed explanation of any steps, or do you have any questions?

Relative Questions:

  1. How do you find the least common multiple (LCM) of several numbers?
  2. What are the steps to isolate a variable in an algebraic equation?
  3. How do you handle equations with fractions?
  4. What is the process for distributing and combining like terms?
  5. How do you simplify fractions to their lowest terms?

Tip:

When working with equations that involve fractions, multiplying through by the least common multiple of the denominators can simplify the process significantly.

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Math Problem Analysis

Mathematical Concepts

Equations
Fractions
Algebra

Formulas

Least Common Multiple (LCM)

Theorems

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Suitable Grade Level

Grades 9-12