Question

complete the sentence based on the equation shown below.
$-3x + 15 = h(-x + 3)$
answer attempt 1 out of 2
this equation will have zero solutions when $h = \square$ because you get zero solutions when you have number of xs on either side of the equation and

Explanation:

Step1: Rearrange left-hand side

Factor out -3 from $-3x + 15$:
$-3x + 15 = -3(x - 5) = 3(-x + 5)$

Step2: Match coefficients for x terms

Set coefficients of $x$ equal:
From $3(-x + 5) = h(-x + 3)$, the coefficient of $x$ on left is $-3$, on right is $-h$. For same x count:
$-h = -3 \implies h=3$

Step3: Check constant terms

When $h=3$, right-hand side is $3(-x+3)=-3x+9$. Left-hand side is $-3x+15$.
$-3x+15=-3x+9$ simplifies to $15=9$, which is false.

Answer:

This equation will have zero solutions when $h=3$ because you get zero solutions when you have the same number of x's on either side of the equation and different constant terms that create a false statement.