Question

question
complete the sentence based on the equation shown below.
\\( h(-x - 2) = -7(x + 2) \\)
answer attempt 1 out of 2
this equation will have one solution when \\( h = \square \\) because you get one solution when
you have \\( \quad \\) number of \\( x \\)s on either side of the equation and
\\( \quad \\).

Explanation:

Step1: Rewrite left-hand side

$h(-x - 2) = -hx - 2h$

Step2: Rewrite right-hand side

$-7(x + 2) = -7x - 14$

Step3: Analyze one-solution condition

For one solution, coefficients of $x$ must differ: $-h
eq -7$

Step4: Solve for $h$

$h
eq 7$; when $h$ is not 7, the number of $x$ terms (coefficients) are unequal, and the constant terms can be anything (but the key is unequal $x$ coefficients).

Answer:

This equation will have one solution when $h = \boldsymbol{\text{any real number except 7}}$ because you get one solution when you have a different number of $x$'s on either side of the equation and the constant terms can be equal or unequal.

(Note: If only a single numerical value is expected in the box, the problem may be phrased to ask for when it does NOT have one solution, but based on the logic of linear equations, the one-solution condition is when the coefficients of $x$ are not equal, so $h
eq 7$.)