Answer:
Yes, Tran is correct .
By substituting different values for x, we can see that [tex]\frac{-1}{4}x[/tex] -7 + [tex]\frac{9}{4}x[/tex] + 2x is equivalent to 4x-7.
Step-by-step explanation:
Lets substitute x = 1 in [tex]\frac{-1}{4}x[/tex] -7 + [tex]\frac{9}{4}x[/tex] + 2x
⇒ [tex]\frac{-1}{4}(1)[/tex] -7 + [tex]\frac{9}{4}(1)[/tex] + 2(1)
⇒ [tex]\frac{-1}{4}[/tex] -7 + [tex]\frac{9}{4}[/tex] + 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 [tex]\frac{-1}{4}x[/tex] -7 + [tex]\frac{9}{4}x[/tex] + 2x
⇒ [tex]\frac{-1}{4}(2)[/tex] -7 + [tex]\frac{9}{4}(2)[/tex] + 2(2).
⇒ [tex]\frac{-1}{2}[/tex] - 7 + [tex]\frac{9}{2}[/tex] + 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, [tex]\frac{-1}{4}x[/tex] -7 + [tex]\frac{9}{4}x[/tex] + 2x is equivalent to 4x-7.
[tex]\frac{-1}{4}x[/tex] -7 + [tex]\frac{9}{4}x[/tex] + 2x
= -7 + [tex]\frac{9-1}{4}x[/tex] + 2x
= -7 + 2x + 2x.
= 4x-7.
