Question

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

Answer 1

Yes, Tran is correct .

By substituting different values for x, we can see that
`(-1)/(4)x` -7 +
`(9)/(4)x` + 2x is equivalent to 4x-7.

Explanation:

Lets substitute x = 1 in
`(-1)/(4)x` -7 +
`(9)/(4)x` + 2x

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

⇒
`(-1)/(4)` -7 +
`(9)/(4)` + 2

⇒ -3.

Now, substitute x = 1 in 4x-7.

⇒ 4(1) - 7 = -3.

⇒ we got -3 in both the cases.

Now let us substitute x = 2 in
`(-1)/(4)x` -7 +
`(9)/(4)x` + 2x

⇒
`(-1)/(4)(2)` -7 +
`(9)/(4)(2)` + 2(2).

⇒
`(-1)/(2)` - 7 +
`(9)/(2)` + 4.

⇒ 1.

now, x =2 in 4x -7.

⇒ 4(2) - 7 = 1.

⇒ we got 1 in both the cases.

Not only these values, for any value of x both the expressions give same value, because,
`(-1)/(4)x` -7 +
`(9)/(4)x` + 2x is equivalent to 4x-7.

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

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

= -7 + 2x + 2x.

= 4x-7.