Question

select the correct answer. 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: Analyze the equation

After expanding, both sides are $-9x - 15$. This means the equation is an identity (true for all $x$), so it has infinitely many solutions.

Answer:

D. The equation has infinitely many solutions.