SOLUTION: Using both the addition principle and multiplication principle, solve: x + 1/4 x=10

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Question 1031138: Using both the addition principle and multiplication principle, solve:
x + 1/4 x=10
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Using both the addition principle and multiplication principle, solve:
x + 1/4 x=10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

I don't know these principles.

I simply do this:

x+%2B+%281%2F4%29x = 10,

%284%2F4%29x+%2B+%281%2F4%29x = 10,

%285%2F4%29%2Ax = 10,

x = %284%2F5%29%2A10,

x = 8.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Fraction skills, too.
x%2B%281%2F4%29x=10
%284%2F4%29x%2B%281%2F4%29x=10
%281%2F4%29x%284%2B1%29=10
%281%2F4%29%285%29x=10-----computation and commutative property
%281%2F4%295%2A%284%29%281%2F5%29x=4%2A%281%2F5%2910----multiplication principle
%281%2F4%29%284%295%281%2F5%29x=4%2A10%2F5----commutative property of multiplication again
highlight%28x=8%29-----simplification computation on right member, multiplicative inverse property on the left member.