Question

which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) - 3x a. the equation has one solution, x = 1. b. the equation has one solution, x = 0. c. the equation has no solution. d. the equation has infinitely many solutions.

Explanation:

Step1: Expand both sides

Left side: $-9(x + 3) + 12 = -9x - 27 + 12 = -9x - 15$
Right side: $-3(2x + 5) - 3x = -6x - 15 - 3x = -9x - 15$

Step2: Compare both sides

After expansion, both sides are $-9x - 15$. This means the equation is an identity, true for all $x$.

Answer:

D. The equation has infinitely many solutions.