Question

Identify the reasoning that would justify each step in solving for m

Answer 1

Given

`(3)/(4)(m-500)=8000+4000`

Notice that the right side of the equation consists of like terms (they do not depend on m). Therefore, Step 1 goes with Combine like terms.

Then,

`(3)/(4)(m-500)=(3)/(4)*m+(3)/(5)(-500)=(3m)/(4)-375\rightarrow\text{ distributive property}`

Step 2 applies the distributive property.

As for the properties of the equality,

`\begin{gathered} a=b\Rightarrow a+c=b+c\rightarrow\text{ addition property of equality} \\ a=b\Rightarrow ac=bc\rightarrow\text{ multiplication property of equality\rbrack} \\ a=b\Rightarrow(a)/(c)=(b)/(c)\rightarrow\text{ division property of inequality} \end{gathered}`

Thus, steps 3 through 5 are:

Step 3 - Addition property

Step 4 - Division property

Step 5 - Multiplication property