Let's review the equation and the steps taken to solve it to understand the justification for Step 3 in the solution of the given equation:
Given:
[tex]\[ \frac{5}{2} h - \frac{15}{2} = \frac{1}{5} h \][/tex]
Here are the steps:
1. [tex]\[ \frac{23}{10} h - \frac{15}{2} = 0 \][/tex]
2. [tex]\[ \frac{23}{10} h = \frac{15}{2} \][/tex]
3. [tex]\[ h = \frac{75}{23} \][/tex]
To determine the justification for Step 3, we need to understand how we arrived at that specific step. In Step 2, we have:
[tex]\[ \frac{23}{10} h = \frac{15}{2} \][/tex]
To isolate [tex]\( h \)[/tex], we must divide both sides of the equation by [tex]\( \frac{23}{10} \)[/tex]. Dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[ h = \frac{\frac{15}{2}}{\frac{23}{10}} = \frac{15}{2} \times \frac{10}{23} = \frac{150}{46} = \frac{75}{23} \][/tex]
This action of dividing both sides by the coefficient of [tex]\( h \)[/tex] (which is [tex]\( \frac{23}{10} \)[/tex]) is consistent with the multiplication property of equality.
Hence, the correct justification for Step 3 is:
the multiplication property of equality.
