Question

find the missing number so that the equation has infinitely many solutions. -5x - 9 = 3(3x - 3) + \square x

Explanation:

Step1: Expand right-hand side

$3(3x - 3) + \square x = 9x - 9 + \square x$

Step2: Combine like terms on RHS

$9x - 9 + \square x = (9 + \square)x - 9$

Step3: Match coefficients of $x$

For infinitely many solutions, coefficients of $x$ on both sides must be equal:
$-5 = 9 + \square$

Step4: Solve for the missing number

$\square = -5 - 9$
$\square = -14$

Answer:

$-14$