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

Answer:

Yes, Tran is correct .

By substituting different values for x, we can see that $\frac{-1}{4}x$ -7 + $\frac{9}{4}x$ + 2x is equivalent to 4x-7.

Step-by-step explanation:

Lets substitute x = 1 in $\frac{-1}{4}x$ -7 + $\frac{9}{4}x$ + 2x

⇒  $\frac{-1}{4}(1)$ -7 + $\frac{9}{4}(1)$ + 2(1)

⇒  $\frac{-1}{4}$ -7 + $\frac{9}{4}$ + 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  $\frac{-1}{4}x$ -7 + $\frac{9}{4}x$ + 2x

⇒  $\frac{-1}{4}(2)$ -7 + $\frac{9}{4}(2)$ + 2(2).

⇒ $\frac{-1}{2}$ - 7 + $\frac{9}{2}$ + 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, $\frac{-1}{4}x$ -7 + $\frac{9}{4}x$ + 2x is equivalent to 4x-7.

$\frac{-1}{4}x$ -7 + $\frac{9}{4}x$ + 2x

= -7 + $\frac{9-1}{4}x$ + 2x

= -7 + 2x + 2x.

= 4x-7.