Question

Is there a value of k for which the equation 2(kx + 2) + 9 = 4(x + k) + 1 has infinitely many solutions? Explain​

Answer 1

The equation 2(kx + 2) + 9 = 4(x + k) + 1 does not have infinitely many solutions.

Step-by-step explanation:

To determine if there is a value of k for which the equation 2(kx + 2) + 9 = 4(x + k) + 1 has infinitely many solutions, we can simplify and solve the equation.

1. Distribute on both sides of the equation: 2kx + 4 + 9 = 4x + 4k + 1.
2. Combine like terms: 2kx + 13 = 4x + 4k + 1.
3. Move all terms involving x to one side and all constant terms to the other side: 2kx - 4x = 4k - 13 - 1.
4. Combine like terms: (2k - 4)x = 4k - 14.
5. Simplify further: 2(k - 2)x = 4(k - 2).
6. Cancel out the common factor of (k - 2) on both sides: 2x = 4.
7. Divide both sides by 2 to solve for x: x = 2.

Therefore, the equation has a unique solution for x = 2, which means there is no value of k for which the equation has infinitely many solutions.