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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 22 Oct 2020, 12:41
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D
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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6)?

A. 1/5
B. 2/5
C. 1
D. 5/2
E. 5
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D
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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 22 Oct 2020, 13:23
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Given: f (x) = 2x − 7,

To find: for what value of x, does 3f(x) − 3 = f (2x − 6)?

Solution:
3(2x-7) -3 = 2(2x-6)-7
6x-21-3 = 4x-12-7
6x-24 = 4x-19
2x = 5
X = 5/2

Answer is D

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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 22 Oct 2020, 15:06
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Bunuel
Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6)?

A. 1/5
B. 2/5
C. 1
D. 5/2
E. 5
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Left side \(= 3*f(x) - 3 = 3(2x - 7) - 3 = 6x - 21 - 3 = 6x - 24\).

Think of the function as \(f(y) = 2y - 7\), when we want to evaluate f(2x - 6) we replace all y's with 2x - 6.

Then \(f(2x - 6) = 2*(2x - 6) - 7 = 4x - 12 - 7 = 4x - 19\).

Finally 6x - 24 = 4x - 19 and 2x = 5.

Ans: D
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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 22 Oct 2020, 20:55
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Bunuel
Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6)?

A. 1/5
B. 2/5
C. 1
D. 5/2
E. 5
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3f (x)-3 = f (2x-6) ---> 3*(2x-7)-3 = 2(2x-6)-7 ---> 6x-24 = 4x-19 ---> 2x=5 x=5/2 D)
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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 27 Oct 2020, 11:35
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Bunuel
Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6)?

A. 1/5
B. 2/5
C. 1
D. 5/2
E. 5
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Solution:

Translating 3f(x) - 3 = f(2x - 6) into a regular equation, we have:

3(2x - 7) - 3 = 2(2x - 6) - 7

6x - 21 - 3 = 4x - 12 - 7

6x - 24 = 4x - 19

2x = 5

x = 5/2

Answer: D
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Given f (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6 15 May 2022, 12:44
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Given that f (x) = 2x − 7 and we need to find for what value of x, does 3f (x) − 3 = f (2x − 6)

3f (x) − 3 = f (2x − 6)

Now, to find the value of f(2x-6) we need to compare what is inside the bracket in f(x) and f(2x-6)
=> to find f(2x-6) we need to replace x with 2x-6 in f(x)
=> f(2x-6) = 2*(2x-6) - 7 = 4x - 12 - 7 = 4x - 19 ...(1)

3f (x) − 3 = f (2x − 6)
=> 3(2x-7) − 3 = 4x-19 [ from (1) ]
=> 6x - 21 - 3 = 4x - 19
=> 6x - 24 = 4x - 19
=> 6x - 4x = 24 - 19
=> 2x = 5
=> x = \(\frac{5}{2}\)

So, Answer will be D
Hope it helps!

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