SOLUTION: The following equation has denominators that contain variables. for this equation write the value or values of the variable that make a denominator zero. these are the restrictions

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Question 1031153: The following equation has denominators that contain variables. for this equation write the value or values of the variable that make a denominator zero. these are the restrictions on the variable. keeping the restrictions in mind, solve the equation.
2/11x + 1/4 = 81/22x - 1/3
My work for solving the equation is (2/11)x + 1/4 = (81/22)x - 1/3
24 x + 33 = 486 x - 44
77 = 462 x
x = 77/462
x = 7/42
x = 1/6
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You very neatly indicated some groupings showing that the denominators contain no variables, so NO RESTRICTION on x is necessary. Did you really have something else?

You began with 2/11x + 1/4 = 81/22x - 1/3 and then you gave clarification of (2/11)x + 1/4 = (81/22)x - 1/3
and as rendered will look like
%282%2F11%29x%2B1%2F4=%2881%2F22%29x-1%2F3.

Lowest common denominator is 3%2A4%2A11;

%283%2A4%2A11%29%28%282%2F11%29x%2B1%2F4%29=%283%2A4%2A11%29%28%2881%2F22%29x-1%2F3%29

6x%2B33=6%2A81x-44

6%2A81x-6x=33%2B44, as combined steps,

6%2881-1%29x=77

6%2A80x=77

480x=77

x=77%2F480

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The following equation has denominators that contain variables. for this equation write the value or values of the variable that make a denominator zero. these are the restrictions on the variable. keeping the restrictions in mind, solve the equation.
2/11x + 1/4 = 81/22x - 1/3
My work for solving the equation is (2/11)x + 1/4 = (81/22)x - 1/3
24 x + 33 = 486 x - 44
77 = 462 x
x = 77/462
x = 7/42
x = 1/6
You're ALMOST correct. highlight_green%28x+=+6%29, not 1%2F6, with x+%3C%3E+0, as x = 0 makes the DENOMINATOR 0 (zero).



You have the equation backwards: Instead of 24x + 33 = 486x - 44. you should've had: 24 + 33x = 486 - 44x