Final answer:
To find the value of k for which the equation has infinitely many solutions, equate the coefficients of x on both sides of the equation and solve for k. The value of k is -15/8.
Step-by-step explanation:
To find the value of k for which the equation has infinitely many solutions, we need to equate the coefficients of x on both sides of the equation. By comparing the coefficients, we have:
16x3(k + 2) = 2x
16k + 32 = 2
16k = -30
k = -30/16 = -15/8
Therefore, the value of k for which the equation has infinitely many solutions is -15/8.
Learn more about Infinite solutions in equations