SOLUTION: Solve the inequality. Write the solution set in interval notation and graph it. 12x - 18 > 3(3x-13)

Algebra ->  Algebra  -> Inequalities -> SOLUTION: Solve the inequality. Write the solution set in interval notation and graph it. 12x - 18 > 3(3x-13)       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 166187: Solve the inequality. Write the solution set in interval notation and graph it.
12x - 18 > 3(3x-13)
Answer by jim_thompson5910(21684) About Me  (Show Source):
You can put this solution on YOUR website!

12x-18%3E3%283x-13%29 Start with the given inequality.


12x-18%3E9x-39 Distribute.


12x%3E9x-39%2B18 Add 18 to both sides.


12x-9x%3E-39%2B18 Subtract 9x from both sides.


3x%3E-39%2B18 Combine like terms on the left side.


3x%3E-21 Combine like terms on the right side.


x%3E%28-21%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3E-7 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is x%3E-7


So the answer in interval notation is


Also, the answer in set-builder notation is


Here's the graph of the solution set

drawing%28500%2C80%2C-17%2C+3%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-17%2C+3%29%2C%0D%0A%0D%0Aarrow%28-7%2C0%2C3%2C0%29%2C%0D%0Aarrow%28-7%2C0.30%2C3%2C0.30%29%2C%0D%0Aarrow%28-7%2C0.15%2C3%2C0.15%29%2C%0D%0Aarrow%28-7%2C-0.15%2C3%2C-0.15%29%2C%0D%0Aarrow%28-7%2C-0.30%2C3%2C-0.30%29%2C%0D%0A%0D%0Acircle%28-7%2C0%2C0.3%29%2C%0D%0Acircle%28-7%2C0%2C0.3%29%2C%0D%0Acircle%28-7%2C0%2C0.3%29%2C%0D%0Acircle%28-7%2C0%2C0.3-0.02%29%0D%0A%29