(1/7x-2/7)(-1/5x+3/5)(1/3x+4/3)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation: (1/7x - 2/7)(-1/5x + 3/5)(1/3x + 4/3) = 0

This equation involves a product of three linear expressions that equals zero. To solve this, we can use the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

Step 1: Apply the Zero Product Property

We can set each of the three linear expressions equal to zero:

• (1/7x - 2/7) = 0
• (-1/5x + 3/5) = 0
• (1/3x + 4/3) = 0

Step 2: Solve for x in each equation

• Equation 1:

  • Add 2/7 to both sides: (1/7x) = 2/7
  • Multiply both sides by 7: x = 2

• Equation 2:

  • Add 1/5x to both sides: (3/5) = (1/5x)
  • Multiply both sides by 5: x = 3

• Equation 3:

  • Subtract 4/3 from both sides: (1/3x) = -4/3
  • Multiply both sides by 3: x = -4

Solution

Therefore, the solutions to the equation (1/7x - 2/7)(-1/5x + 3/5)(1/3x + 4/3) = 0 are x = 2, x = 3, and x = -4.