Question

select the correct answer.
what is the justification for step 3 in the solution process?
\\(\frac{5}{2}h - \frac{15}{2} = \frac{1}{5}h\\)
step 1 : \\(\frac{23}{10}h - \frac{15}{2} = 0\\)
step 2 : \\(\frac{23}{10}h = \frac{15}{2}\\)
step 3 : \\(h = \frac{75}{23}\\)
\\(\circ\\) the subtraction property of equality
\\(\circ\\) combining like terms
\\(\circ\\) the multiplication property of equality
\\(\circ\\) the addition property of equality

Explanation:

To find the justification for Step 3, we analyze the transformation from Step 2 ($\frac{23}{10}h = \frac{15}{2}$) to Step 3 ($h=\frac{75}{23}$).

• The multiplication property of equality states that if we multiply both sides of an equation by the same non - zero number, the equation remains true.
• In Step 2, we have $\frac{23}{10}h=\frac{15}{2}$. To isolate $h$, we multiply both sides of the equation by the reciprocal of $\frac{23}{10}$, which is $\frac{10}{23}$.
• Multiplying the left - hand side: $\frac{23}{10}h\times\frac{10}{23}=h$.
• Multiplying the right - hand side: $\frac{15}{2}\times\frac{10}{23}=\frac{15\times10}{2\times23}=\frac{150}{46}=\frac{75}{23}$.
• The subtraction property of equality involves subtracting the same number from both sides, which is not what's happening here. Combining like terms is about combining terms with the same variable or constant terms, and this is not a case of combining like terms. The addition property of equality involves adding the same number to both sides, which is also not the case here. So the justification is the multiplication property of equality.

Answer:

the multiplication property of equality