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.