Given \(f(x) = 3x - 5,\) for what value of \(x\) does \(2\cdot f(x) - 1 = f(3x - 6).\)

[VJesus12]

Given \(f(x) = 3x - 5,\) for what value of \(x\) does \(2\cdot f(x) - 1 = f(3x - 6).\)

A. 0
B. 4
C. 6
D. 7
E. 13

Answer: B

Source: Magoosh

[jhavyom]

Given \(f(x) = 3x - 5,\) for what value of \(x\) does \(2\cdot f(x) - 1 = f(3x - 6).\)

A. 0
B. 4
C. 6
D. 7
E. 13

Answer: B

Source: Magoosh

f(x) = 3x - 5
f(3x-6) = 3(3x-6) - 5

Now, 2f(x) - 1 = f(3x-6)
2(3x - 5) - 1 = 3(3x-6) - 5
6x - 10 - 1 = 3(3x-6) - 5
6x - 11 = 9x - 18 -5
3x = 12
x = 4

Option B is the answer.

[Scott@TargetTestPrep]

Given \(f(x) = 3x - 5,\) for what value of \(x\) does \(2\cdot f(x) - 1 = f(3x - 6).\)

A. 0
B. 4
C. 6
D. 7
E. 13

Answer: B

Solution:

Since f(x) = 3x - 5, then f(3x - 6) = 3(3x - 6) - 5 = 9x - 18 - 5 = 9x - 23, and we have:

2(3x - 5) - 1 = 9x - 23

6x - 10 - 1 = 9x - 23

12 = 3x

4 = x

Answer: B