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# let f(x)=(2-3x)/(5-2x). For what value of a is f(a)=3.

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let f(x)=(2-3x)/(5-2x).  For what value of a is f(a)=3.

WhichWitchIsWhich  Oct 30, 2017

#1
+6945
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f(x)  =  (2 - 3x) / (5 - 2x)

f(a)  =  (2 - 3a) / (5 - 2a)  =  3

(2 - 3a) / (5 - 2a)  =  3

Multiply both sides by  (5 - 2a) .

2 - 3a  =  3(5 - 2a)                    And  a ≠ 5/2  .

Distribute the  3 .

2 - 3a  =  15 - 6a

Add  6a  to both sides.

2 + 3a  =  15

Subtract  2  from both sides.

3a  =  13

Divide both sides by  3 .

a  =  13/3

hectictar  Oct 30, 2017
edited by hectictar  Oct 30, 2017
Sort:

#1
+6945
+1

f(x)  =  (2 - 3x) / (5 - 2x)

f(a)  =  (2 - 3a) / (5 - 2a)  =  3

(2 - 3a) / (5 - 2a)  =  3

Multiply both sides by  (5 - 2a) .

2 - 3a  =  3(5 - 2a)                    And  a ≠ 5/2  .

Distribute the  3 .

2 - 3a  =  15 - 6a

Add  6a  to both sides.

2 + 3a  =  15

Subtract  2  from both sides.

3a  =  13

Divide both sides by  3 .

a  =  13/3

hectictar  Oct 30, 2017
edited by hectictar  Oct 30, 2017

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