To complete the sentence based on the equation \( 2x - 6 = hx - 6 \), we can simplify the equation. First, we notice that both sides have \(-6\), so we can add \(6\) to both sides:
\( 2x = hx \)
Next, we can rearrange this equation:
\( 2x - hx = 0 \)
Factoring out \(x\), we get:
\( x(2 - h) = 0 \)
This leads us to the conclusion that either \(x = 0\) or \(2 - h = 0\) (which means \(h = 2\)).
Therefore, we can complete the sentence as follows:
"Based on the equation \( 2x - 6 = hx - 6 \), the solutions are either \(x = 0\) or \(h\) must equal \(2\)."