Question

Complete the sentence based on the equation shown below. h, of, minus, 3, x, plus, 6, equals, minus, 12, x, plus, 24 h(−3x+6)= −12x+24 Answer Attempt 1 out of 2 This equation will have infinitely many solutions when h, equalsh= because you get infinitely many solutions when you have number of x's on either side of the equation and .

Answer 1

The equation will have infinitely many solutions when \( h = -12 \) because you get infinitely many solutions when you have the same coefficient of \( x \) on either side of the equation, and the constant terms are also equal.

To set it up, we want the expressions on both sides to be equivalent:

\[
h(-3x + 6) = -12x + 24
\]

For this to have infinitely many solutions, the coefficients of \( x \) must match:

\[
h(-3) = -12 \implies h = 4
\]

And the constant terms must also be equal when substituting \( h = 4 \):

\[
h \cdot 6 = 24 \implies 4 \cdot 6 = 24
\]

Thus, \( h = 4 \) ensures there are infinitely many solutions.