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For what values of a and b would the equation have infinitely many solutions in the equation 6 + 3(6x - 7) = ax + b?

User Jeto
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Final answer:

The values of a and b for which the equation 6 + 3(6x - 7) = ax + b has infinitely many solutions are a = 18 and b = -15, which align the coefficients and constants on both sides of the equation.

Step-by-step explanation:

To find the values of a and b for which the equation 6 + 3(6x - 7) = ax + b has infinitely many solutions, we first need to simplify and compare coefficients. The equation simplifies as follows:

  • 6 + 3(6x - 7) = ax + b
  • 6 + 18x - 21 = ax + b
  • 18x - 15 = ax + b

For the equation to have infinitely many solutions, the coefficients of x must be the same on both sides, and the constant terms must also be the same. Thus:

  • For x: 18 = a
  • For the constant term: -15 = b

Therefore, the values a = 18 and b = -15 will yield an equation with infinitely many solutions.

User Muckabout
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