Question 70626
{{{3(2-3x)>5(x-2(x+5))}}}
.
Start by treating this just as you would an equation and solve for x.  First multiply out
the left side.  When you do the result is:
.
{{{6-9x>5(x-2(x+5))}}}
.
Next on the right side multiply out the -2 times (x+5).  When you do the inequality 
becomes:
.
{{{6-9x>5(x-2x-10)}}}
.
Then on the right side combine the x and -2x to get just -x. The inequality is then:
.
{{{6-9x>5(-x-10)}}}
.
Finally multiply out the right side:
.
{{{6-9x>-5x-50}}}
.
To cancel out the +6 on the left side, add a negative 6 to both sides.  The inequality is
then"
.
{{{-9x>-5x-56}}}
.
And to cancel out the -5x on the right side, add +5x to both sides.  The result is:
.
{{{-4x>-56}}}
.
To solve this for positive x, divide both sides by -4.  But now you have to remember the
rule ... whenever you divide or multiply both sides of an inequality by a negative number,
the inequality reverses direction.  Dividing by -4 and reversing the inequality gives you:
.
{{{x<14}}}
.
This tells you that when x is less than 14 the inequality of the original problem is 
satisfied. And when x is 14 or more, the inequality of the original problem will not work.
.
Try a few values of x less than 14 and see if they don't work. Try x=14 and see why it doesn't
work. And try a value or two for x greater than 14 to verify that they don't work.
.
Note 0 is less that 14, so you can try it.  It makes all the x's disappear and the problem
is simplified because of that.
.
Hope this helps you understand inequalities a little better. And don't forget the rule
about multiplying or dividing inequalities by a negative number.