Question

Complete the sentence based on the equation shown below.
h (-2x + 8) = -12 (x - 4)
This equation will have one solution when h, = blank because you get one solution when you have blank number of x's on either side of the equation and blank
.

Answer 1

Fill in the blank

Answer 2

To complete the sentence based on the equation \( h (-2x + 8) = -12 (x - 4) \), we first need to determine the conditions under which this equation will have one solution.

Let's start by simplifying both sides of the equation:

1. Expand the right side:
\(-12 (x - 4) = -12x + 48\)

So, the equation now looks like:
\[ h (-2x + 8) = -12x + 48 \]

Now, we can rewrite the left side as:
\[ -2hx + 8h = -12x + 48 \]

Next, let's organize the terms involving \( x \):

1. Move all the terms involving \( x \) to one side:
\[ -2hx + 12x = 48 - 8h \]

2. Factor out \( x \):
\[ x(-2h + 12) = 48 - 8h \]

To have one solution in an equation like this, we want the coefficient of \( x \) to be non-zero (which will allow for exactly one solution). Thus the equation will have one solution when:

\[ -2h + 12 \neq 0 \]
Solving for \( h \):
\[ -2h + 12 = 0 \]
\[ -2h = -12 \]
\[ h = 6 \]

The inequality we need is \( h \neq 6 \).

Now, putting this all together, the sentence would read:

"This equation will have one solution when \( h \neq 6 \) because you get one solution when you have one number of \( x's \) on either side of the equation and a constant."

Answer 3

Based on the analysis provided, here is a completion of the sentence with the appropriate blanks filled in:

"This equation will have one solution when **h ≠ 6** because you get one solution when you have **one** number of x's on either side of the equation and **a constant**."