Question

Complete the sentence based on the equation shown below.
start fraction, 3, divided by, 2, end fraction, x, minus, 5, equals, start fraction, 3, divided by, 2, end fraction, x, plus, h
2
3
​
x−5=
2
3
​
x+h
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

This equation will have infinitely many solutions when \( h = -5 \) because you get infinitely many solutions when you have the same number of \( x \)'s on either side of the equation and the constant terms are also equal.

To explain further:

Starting with the original equation:

\[
\frac{3}{2} x - 5 = \frac{3}{2} x + h
\]

For the \( x \) terms to be equal on both sides, we see that both contain \( \frac{3}{2} x \). Therefore, for the equation to hold true for all \( x \), the constant terms must also be equal, that is:

\[
-5 = h
\]

Thus, \( h \) must equal \(-5\) for the equation to have infinitely many solutions.