We have that we are solving for the equation:
[tex]3x-6=x+4[/tex]To start solving it, we need to subtract x to both sides of the equation. This property is Subtraction Property of Equality:
[tex]3x-x-6=x-x+4\Rightarrow2x-6=4[/tex]In the next step, we use the Addition Property of Equality, since we have to add 6 to both sides of the equation:
[tex]2x-6+6=4+6\Rightarrow2x=10[/tex]And the last step is to use the Division Property of Equality since we need to divide by 2 to both sides of the equation:
[tex]2x=10\Rightarrow\frac{2x}{2}=\frac{10}{2}\Rightarrow x=5[/tex]In summary, the order of each of the reasons for each step is (see all the steps above):
• The original equation is 3x - 6 = x + 4
,• After applying the Subtraction Property of Equality, we got 2x - 6 = 4
,• After applying the Addition Property of Equality, we got 2x = 10
,• After applying the Division Property of Equality, we finally got x = 5.
