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Let \(f(x) = \begin{cases} 9x+16 &\text{if }x<2, \\ 2x-14&\text{if }x\ge2. \end{cases} \)If f(x)=-2, find the sum of all possible values of x.

 

Please help me, how am I supposed to proceed with this?

 Jun 9, 2020
 #1
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Since  f(x)  =  2, there are two ways that the answer is 2.

First way:       if x < 2:   9x + 16  =  2   --->   9x  =  -14    --->   x  =  -14/9.

Second way:  if x >= 2:  2x - 14  =  2   --->   2x  =  16     --->   x  =  8

 

You will now need to add the two possible values for x ...

 Jun 9, 2020
 #2
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Oh, so what I do is just plug in the value -2 for 9x+16 and 2x-14?

By the way, there's a mistake because f(x)= -2, not 2.

 Jun 9, 2020
 #4
avatar+21955 
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Thanks --  I read it as 2, not -2:

 

First:      9x + 16  =  -2   --->   9x  =  -18   --->   x  =  -2

Second:  2x - 14  =  -2   --->   2x  =  12    --->   x  =  6

 

To "find the sum of all possible values of x"

-- there are only two ways; either x  =  -2  or  x  =  6

So, to find the sum, the answer is:  -2 + 6  =  4.

geno3141  Jun 9, 2020
 #3
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I meant plug in the value -2 = 9x+16 and 2x-14.

 Jun 9, 2020
 #5
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Okay that makes a lot more sense now. Thanks for the help!

 Jun 9, 2020

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