Answer:
Explanation:
To have infinitely many solutions, the equation must be an identity, meaning the left-hand side of the equation is equal to the right-hand side for all values of x. In order for this to be true, the coefficients of x on both sides of the equation must be equal.
So, let's simplify the equation and compare the coefficients of x:
2/3(9x - 3) = 2(3x - a)
Multiplying both sides by 3/2, we get:
9x - 3 = 3(3x - a)
Expanding the right-hand side, we get:
9x - 3 = 9x - 3a
Comparing the coefficients of x on both sides, we see that they are equal. Therefore, the value of a that would make the equation an identity and have infinitely many solutions is any value of a, since it would not affect the equality of the coefficients of x.
To confirm, let's substitute a value for a and simplify the equation:
Let's say a = 5. Then:
2/3(9x - 3) = 2(3x - 5)
6x - 2 = 6x - 10
Simplifying further, we get:
-2 = -10
Since this statement is clearly false, we see that the value of a does not affect the equality of the coefficients of x, and therefore any value of a would make the equation have infinitely many solutions.