Question

question
complete the sentence based on the equation shown below.
$2x - 5 = hx + 6$
answer attempt 1 out of 2
this equation will have zero solutions when $h = \square$ because you get zero solutions when you
have $\quad$ number of xs on either side of the equation and
$\quad$.

Explanation:

Step1: Rearrange the equation

$2x - hx = 6 + 5$

Step2: Factor out x

$x(2 - h) = 11$

Step3: Analyze no-solution condition

For zero solutions, the coefficient of $x$ must be 0 (so the left side becomes 0) while the right side is non-zero. Set $2 - h = 0$.
$2 - h = 0 \implies h=2$
When $h=2$, the equation becomes $0=11$, which is false, so no solutions exist when the number of $x$ terms are equal, but the constant terms are unequal.

Answer:

This equation will have zero solutions when $h = 2$ because you get zero solutions when you have the same number of x's on either side of the equation and different constant terms (or unequal constant values).