Question

question 6 of 8
select the correct answer.
what is the justification for step 3 in the solution process?
\\(\frac{3}{5}h - \frac{4}{3} = \frac{1}{4}\\)
step 1 : \\(\frac{36}{60}h - \frac{80}{60} = 0\\)
step 2 : \\(\frac{36}{60}h = \frac{80}{60}\\)
step 3 : \\(h = \frac{80}{36}\\)
\\(\circ\\) the addition property of equality
\\(\circ\\) combining like terms
\\(\circ\\) the subtraction property of equality
\\(\circ\\) the multiplication property of equality

Explanation:

To determine the justification for Step 3, we analyze the operations. In Step 2, we have \(\frac{8}{10}h=\frac{4}{2}\). To solve for \(h\), we need to isolate \(h\). 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. Here, we multiply both sides of \(\frac{8}{10}h=\frac{4}{2}\) by the reciprocal of \(\frac{8}{10}\) (or divide both sides by \(\frac{8}{10}\), which is equivalent to multiplying by \(\frac{10}{8}\)), which is an application of the multiplication property of equality. Combining like terms is used when we have similar terms (like \(3x + 5x\)), which is not the case here. The addition/subtraction properties are for adding/subtracting the same number to both sides, not for isolating a variable multiplied by a fraction.

Answer:

the multiplication property of equality