Question 133579
Solve for x:
1) You solve an inequality just as you would solve an equation, with one exception. When you multiply or divide by a negative quantity in the process of solving, you must reverse the inequalitity sign. You don't have any that require this here.
{{{2(2x-3) < 6}}} Divide both sides by 2.
{{{2x-3 < 3}}} Add 3 to both sides.
{{{2x < 6}}} Finally, divide both sides by 2.
{{{x < 3}}} Solution: {x|x<3}

2)
{{{3(3+4x)-8 >= 109}}} Add 8 to both sides.
{{{3(3+4x) >= 117}}} Divide both sides by 3.
{{{3+4x >= 39}}} Subtract 3 from both sides.
{{{4x >= 36}}} Finally, divide both sides by 4.
{{{x >= 9}}} Solution: {x|x>/=9}
3)
{{{3(2y-7) > 4(3y+4)}}} Apply the distributive property to both sides.
{{{6y-21 > 12y+16}}} Subtract 6y from both sides.
{{{-21 > 6y+16}}} Now subtract 16 from both sides.
{{{-37 > 6y}}} Finally, divide both sides by 6.
{{{-6.167 > y}}} Solution: {y|y<-6.167}