Question

complete the sentence based on the equation shown below.
\\(\frac{3}{2}x + 3 = hx + 3\\)
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 $\frac{3}{2}x + 3 = hx + 3$, set coefficients of $x$ equal:
$\frac{3}{2} = h$

Step3: Verify constant terms

The constant terms on both sides are $3$, which are equal.

Answer:

This equation will have infinitely many solutions when $h = \frac{3}{2}$ 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.