Question

complete the sentence based on the equation shown below.
\\( h\left(-3x - 9\
ight)=-9\left(x + 3\
ight) \\)
answer attempt 1 out of 2
this equation will have infinitely many solutions when \\( h = \square \\) because you get infinitely many solutions when you have \\( \quad \\) number of xs on either side of the equation and \\( \quad \\).

Explanation:

Step1: Factor left side's constant

Factor $-3$ from $-3x-9$:
$h(-3(x+3)) = -9(x+3)$

Step2: Simplify left side expression

Multiply $h$ and $-3$:
$-3h(x+3) = -9(x+3)$

Step3: Solve for $h$

Set coefficients equal for infinite solutions:
$-3h = -9$
$h = \frac{-9}{-3} = 3$

Step4: Identify infinite solution conditions

Infinite solutions require equal $x$ coefficients and equal constant terms (after simplifying, both sides become identical).

Answer:

This equation will have infinitely many solutions when $h = 3$ because you get infinitely many solutions when you have the same number of $x$'s on either side of the equation and the same constant terms on both sides.