SOLUTION: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding. x/4 - x-1/2 >= 3

Algebra ->  Inequalities -> SOLUTION: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding. x/4 - x-1/2 >= 3       Log On


   

Question 1068497: Solve the following equations and inequality for x. If the solution is extraneous, please state that it is. Please show me all work for a better understanding.
x/4 - x-1/2 >= 3
Note: x-1 is the whole numerator of the second fraction. All of it is over 2. It is not x - 1/2. If you can not understand '>=', I am trying to state "Greater than or equal to".
Thank you kindly.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What you are describing will be in pure text as x/4-(x-1)/2>=3.
When put inside the triple curly bracket rendering tags, x%2F4-%28x-1%29%2F2%3E=3.

The fraction skills you've already learned also work here. LCD is 4.

x%2F4-%28%28x-1%29%2F2%29%282%2F2%29%3E=3

x%2F4-2%28x-1%29%2F4%3E=3

%28x-2x%2B2%29%2F4%3E=3

-x%2B2%3E=12

-x%3E=10
multiply both sides by negative 1;
highlight%28x%3C=-10%29


NOTE: the faster way to solve this is to multiply BOTH SIDES of the inequality by the LCD of 4. This clears the denominators.