To find the correct justification for step 3 in the solution process, let's carefully analyze each step:
Step 1:
[tex]\[
\frac{23}{10}h - \frac{15}{2} = 0
\][/tex]
To isolate the term with [tex]\( h \)[/tex],
Step 2:
we add [tex]\(\frac{15}{2}\)[/tex] to both sides:
[tex]\[
\frac{23}{10}h = \frac{15}{2}
\][/tex]
This isolates the term with [tex]\( h \)[/tex] on the left side of the equation.
Step 3:
Next, to solve for [tex]\( h \)[/tex], we need to isolate [tex]\( h \)[/tex] completely by getting rid of the coefficient [tex]\(\frac{23}{10}\)[/tex]. We do this by multiplying both sides by the reciprocal of [tex]\(\frac{23}{10}\)[/tex], which is [tex]\(\frac{10}{23}\)[/tex]:
[tex]\[
h = \left(\frac{15}{2}\right) \times \left(\frac{10}{23}\right)
\][/tex]
We multiply on the right side to get:
[tex]\[
h = \frac{150}{46} = \frac{75}{23}
\][/tex]
Thus, the justification for Step 3 is the application of the multiplication property of equality. Therefore, the correct answer is:
[tex]\[
\text{the multiplication property of equality}
\][/tex]
