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: Compare both sides

After expanding, both sides are equal: $-9x - 15=-9x - 15$. This means the equation is true for all real numbers \( x \), so there are infinitely many solutions.

Answer:

D. The equation has infinitely many solutions.