Question

For what values of a and b would make the equation have infinite solutions in 4 + 2(5x - 8) = ax + b?

a) a = 8, b = 12
b) a = 4, b = 0
c) a = 0, b = 4
d) a = 2, b = 8

Answer 1

The equation 4 + 2(5x - 8) = ax + b will have infinite solutions if a = 10 and b = -12 by equating the coefficients of 'x' and the constant terms on both sides. However, none of the provided options match these values.

Step-by-step explanation:

The question asks for what values of a and b the equation will have infinite solutions in 4 + 2(5x - 8) = ax + b. To solve this, we need to simplify the left-hand side (LHS) of the equation and compare it to the right-hand side (RHS).

First, distribute the '2' on the LHS:

4 + 2(5x - 8) = 4 + 10x - 16

Now combine like terms:

10x - 12 = ax + b

For the equation to have infinite solutions, the coefficients of 'x' and the constant terms on both sides must be equal. This means:

a must be equal to 10 (the coefficient of x on the LHS), and b must be equal to -12 (the constant term on the LHS).

However, none of the provided options has both a = 10 and b = -12. Therefore, there is an error in the question as none of the given options (a-d) are correct for the equation to have infinite solutions.