Complete the sentence based on the equation shown below.

Question

h, of, 2, x, plus, 2, equals, 8, left parenthesis, x, minus, 9, right parenthesis
h(2x+2)=
8(x−9)

This equation will have one solution when h,=____because you get one solution when you have_____
number of x's on either side of the equation and___________

Answer 1

To complete the sentence based on the equation \( h(2x+2) = 8(x-9) \), we can determine the conditions under which the equation has one solution.

The equation is effectively a linear equation in \( x \) as long as \( h \) is a non-zero constant. If \( h = 0 \), the left side becomes zero, which would lead to a different form.

Here’s the completed sentence:

This equation will have one solution when \( h \) = a non-zero constant because you get one solution when you have the same number of x's on either side of the equation and the coefficients are such that they do not cancel each other out or lead to a contradiction.

To summarize:

• \( h \) should be a non-zero constant.
• You need the same number of \( x \)'s (usually one) in the expressions.
• The equation should not simplify to an identity or a contradiction.