Question

complete the sentence based on the equation shown below.
$x - 4 = hx - 4$
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 xs on either side of the equation and \quad.

Explanation:

Step1: Rearrange the equation

$x - hx = -4 + 4$

Step2: Factor out $x$

$x(1 - h) = 0$

Step3: Analyze for one solution

For exactly one solution, the coefficient of $x$ cannot be 0 (if $1-h=0$, all $x$ are solutions). So $1-h
eq 0$, meaning $h
eq 1$. When $h
eq 1$, $x = \frac{0}{1-h} = 0$, which is one unique solution. This occurs when there is an **equal** number of $x$ terms only if coefficients are different? No, correction: When coefficients of $x$ are different (unequal number of effective $x$ terms), we get one solution. Wait, rephrase: When we have an **unequal** number of $x$'s on either side (i.e., coefficients of $x$ are not equal) and the constant terms are equal (here, -4 = -4), we get one unique solution.

Answer:

This equation will have one solution when $\boldsymbol{h
eq 1}$ because you get one solution when you have an unequal number of x's on either side of the equation and the constant terms are equal.

(Note: If the blank requires a specific value, but logically any $h$ except 1 works. If forced to a single value, any non-1 number is valid, e.g., $h=0$ is a valid example, but the general case is $h
eq 1$.)