Question

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.

Answer 1

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)