Question

Move a property to each blank box to show the reason for each step.StepProperty3x - 6 = x + 42x - 6 = 42x = 10x=5

Answer 1

We have that we are solving for the equation:

`3x-6=x+4`

To start solving it, we need to subtract x to both sides of the equation. This property is Subtraction Property of Equality:

`3x-x-6=x-x+4\Rightarrow2x-6=4`

In the next step, we use the Addition Property of Equality, since we have to add 6 to both sides of the equation:

`2x-6+6=4+6\Rightarrow2x=10`

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:

`2x=10\Rightarrow(2x)/(2)=(10)/(2)\Rightarrow x=5`

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.