Sure! Let's walk through the steps of the given equation:
Given equation:
[tex]\[
\frac{5}{2} h - \frac{15}{2} = \frac{1}{5} h
\][/tex]
Step 1:
Move all terms involving [tex]\(h\)[/tex] to one side of the equation by subtracting [tex]\(\frac{1}{5}h\)[/tex] from both sides:
[tex]\[
\frac{5}{2} h - \frac{1}{5} h - \frac{15}{2} = 0
\][/tex]
Now, find a common denominator for the fractions involving [tex]\(h\)[/tex]. The least common multiple of 2 and 5 is 10:
[tex]\[
\left( \frac{5 \times 5}{2 \times 5} \right) h - \left( \frac{1 \times 2}{5 \times 2} \right) h - \frac{15}{2} = 0
\][/tex]
[tex]\[
\frac{25}{10} h - \frac{2}{10} h - \frac{15}{2} = 0
\][/tex]
Combine the [tex]\(h\)[/tex] terms:
[tex]\[
\frac{23}{10} h - \frac{15}{2} = 0
\][/tex]
This completes Step 1.
Step 2:
Isolate the variable term [tex]\(\frac{23}{10}h\)[/tex] by adding [tex]\(\frac{15}{2}\)[/tex] to both sides of the equation:
[tex]\[
\frac{23}{10}h = \frac{15}{2}
\][/tex]
This addition step allows us to move the constant term to the other side of the equation.
Step 3:
Solve for [tex]\(h\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{23}{10}\)[/tex]:
[tex]\[
h = \frac{15}{2} \times \frac{10}{23}
\][/tex]
Simplify the multiplication to find [tex]\(h\)[/tex]:
[tex]\[
h = \frac{75}{23}
\][/tex]
The key step between Step 1 and Step 2 is the justification for isolating the variable term. By adding [tex]\(\frac{15}{2}\)[/tex] to both sides, we used the following principle:
The correct justification is:
[tex]\[
\text{the addition property of equality}
\][/tex]
Thus, by following these steps, you can see that the answer to the question is:
[tex]\[
\boxed{\text{the addition property of equality}}
\][/tex]
