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

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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Thu Oct 29, 2020 11:39 am

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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

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Source: Beat The GMAT — Problem Solving | Thu Oct 29, 2020 11:39 am

jhavyom: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Oct 02, 2020 9:16 am

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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