Question

Tran says that -1/4x-7+9/4x+2x id equalvalent to 4x-7. How can substituting any value for x help you determine whether Tran is correct? Is Tran correct? Use substition to justify your answer

Answer 1

You can determine if Tran is correct by substituting any value to "x" into each expression. If the values obtained are equal, then the expressions are equivalent.

Yes, Tran is correct (See explanation).

Explanation:

By definition, equivalent expressions havee the same value.

In this case, given the expression:

`-(1)/(4)x-7+(9)/(4)x+2x`

And the expression:

`4x-7`

We can determine if they are equivalent by giving any value to "x", substituting into each expression and evaluate. If the values obtained are equal, then the expressions are equivalent.

To check if Tran is correct, we can give the following value to "x":

`x=1`

Substituting this value into the expression
`-(1)/(4)x-7+(9)/(4)x+2x`, we get:

`-(1)/(4)(1)-7+(9)/(4)(1)+2(1)=-3`

Substituting
`x=1` into the expression
`4x-7`, we get:

`4(1)-7=-3`

Therefore, we can conclude that Tran is correct.