This equation will have zero solutions when \( h = -8 \) because you get zero solutions when you have the same number of \( x \)'s on either side of the equation and the constant terms do not match.
To elaborate:
- The left-hand side of the equation simplifies to \( -8x - 24 \).
- The right-hand side, depending on the form of \( h(-x + 10) \), will produce another expression in terms of \( x \).
If \( h = -8 \), then the right-hand side becomes:
\[ -8(-x + 10) = 8x - 80 \]
Setting the two expressions equal to each other:
\[ -8x - 24 = 8x - 80 \]
When isolating \( x \), we can combine like terms:
\[ -8x - 8x = -80 + 24 \]
This simplifies to:
\[ -16x = -56 \]
Solving for \( x \), we find:
\[ x = \frac{56}{16} = 3.5 \]
However, if \( h \) does not equal -8, the coefficients of \( x \) on both sides would be different, resulting in a possible solution for \( x \). Therefore, when \( h = -8 \), the resulting equation will have the same coefficients for \( x \) but different constant terms, leading to zero solutions.
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