Question

complete the sentence based on the equation shown below.
\\(10x - 1 = hx - 1\\)
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: Recall infinite solutions rule

A linear equation $ax + b = cx + d$ has infinitely many solutions if $a=c$ and $b=d$.

Step2: Match coefficients of $x$

For $10x - 1 = hx - 1$, set $10 = h$ to match $x$ coefficients.

Step3: Verify constant terms

The constant terms $-1=-1$ are already equal.

Answer:

This equation will have infinitely many solutions when $h = 10$ because you get infinitely many solutions when you have the same number of x's on either side of the equation and the same constant terms on both sides.