Question

Complete the sentence based on the equation shown below.
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.