Question

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

Explanation:

Step1: Isolate x terms

Subtract $2x$ from both sides:
$2x - 2 - 2x = 2x + h - 2x$
Simplify to get: $-2 = h$

Step2: Identify infinite solution condition

For infinite solutions, after simplifying, both sides of the equation must be identical (a true statement for all $x$). This requires the constant terms to match once the $x$ terms are equal (which they already are, as $2x=2x$).

Answer:

This equation will have infinitely many solutions when $h = -2$ because you get infinitely many solutions when you have the same number of x's on either side of the equation and identical constant terms on both sides.