Mariah H.

asked • 06/12/16

Solve 3/4=1/2+5/3x

Please help me solve this equation 

1 Expert Answer

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Mark M. answered • 06/12/16

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3/4 = 1/2 + 5/3x
9 = 6 + 20/x            multiply both sides by 12
9x = 6x + 20            multiply both sides by x
3x = 20                    subtract 6x from both sides
x = 20/3
 
Check
 
3/4 = 1/2 + 5/3(20/3)
3/4 = 1/2 + 5/20
3/4 = 1/2 + 1/4
3/4 = 3/4
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Kenneth S.

3/4 = 1/2 + 5/3x    
According to PEMDAS, the last term is (5/3)x, in which case the solution will be different from Mark's solution.
 
I find that MANY times students fail to group a denominator in parentheses when it's not just a single constant or variable.  Mark has assumed that x belongs in the denominator.
 
Mariah, is the variable x part of the denominator in the last term of your equation?
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06/12/16

Mark M.

PEMDAS has to do with the order of operations, not the order of inscription.
As written 3x is in the denominator. It is not an assumption.
Two was in insure the x is in the numerator: 5x/3 or (5/3)x
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06/13/16

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