Expert: Lynn Houston - 10/27/2010

Question
I have a couple questions on this math. I am not understanding it and the teacher really doesn't have the patience. I am in college and falling behind. Please help me.
Thank you

1) 1/2x-2>3/4x+7.. solve the inequalities and graph
2) 2L=4W-7 solve for W

Answer
The "secret" to solving these are to isolate the variable you're solving for by "undoing" everything that is done to it.  Multiplication undoes division and addition undoes subtraction (and vice versa).  So for the first problem, start multiplying everything by 4x (to get rid of the fractions)  This is assuming that it is the fraction - 2 or the fraction + 7 and that the 2 and 7 are not part of the denominators.

1/2x-2>3/4x+7  
4x/2x - 2(4x) > 3(4x)/4x + 7(4x)  multiply and reduce
2 - 8x > 3 + 28x  add 8x to both sides
2-8x+8x > 3 + 28x + 8x
2>3+36x  subtract 3 from both sides
-1 > 36x  and lastly, divide both sides by 36

-1/36 > x

To graph that, draw a vertical line (with an arrow on both ends) at
x = -1/36, then, pick a number on each side of the line and determine if the equation is true using that number.  So, pick 1.  1 is NOT less than -1/36, so that is not the solution side.  How about -1?  -1 IS less than -1/36 so shade to the left of the line (indicating the solution set).

2L=4W-7  add 7 to both sides
2L + 7 = 4w  divide by 4
(2L + 7)/4 = w

make sense?