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which property justifies the statement? if 5x+2=2x+11,then 5x=2x+9.Addition property of equality,transitive property,symmetric property,subtraction property of equality.

1 Answer

5 votes

Notice the following properties of equality:

1. The Addition property of equality states that, if:


a=b

Then:


a+c=b+c

2. The Subtraction property of equality states that, if:


a=b

Then:


a-c=b-c

3. The Transitive property of equality states that, if:


a=b\text{ and }b=c

Then:


a=c

4. The Symmetric property of equality states that, if:


a=b

Then:


b=a

For this case, you have the following equation:


5x+2=2x+11

If you subtract 2 from both sides of the equation, you are applying the Subtraction property of equality:


\begin{gathered} 5x+2-(2)=2x+11-(2) \\ 5x=2x+9 \end{gathered}

Therefore, the answer is: Last option (Subtraction property of equality)

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