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

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

by jhavyom » Sun Nov 01, 2020 2:22 am
VJesus12 wrote: ↑
Thu Oct 29, 2020 11:39 am
 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.
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Re: Given \(f(x) = 3x - 5,\) for what value of \(x\) does \(2\cdot f(x) - 1 = f(3x - 6).\)

by Scott@TargetTestPrep » Thu Nov 12, 2020 7:36 am
VJesus12 wrote: ↑
Thu Oct 29, 2020 11:39 am
 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

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