SOLUTION: Solve the inequality. State the solution set in interval notation and sketch its graph. 1/6 - 1/3t > 0

Algebra ->  Linear-equations -> SOLUTION: Solve the inequality. State the solution set in interval notation and sketch its graph. 1/6 - 1/3t > 0      Log On


   

Question 134247: Solve the inequality. State the solution set in interval notation and sketch its graph.
1/6 - 1/3t > 0
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F6-%281%2F3%29t%3E0 Start with the given inequality



%286%29%281%2Fcross%286%29-%281%2Fcross%283%29%29t%29=%286%29%280%29 Multiply both sides by the LCM of 6. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



1-2t=0 Distribute and multiply the LCM to each side



-2t%3E0-1Subtract 1 from both sides


-2t%3E-1 Combine like terms on the right side


t%3C%28-1%29%2F%28-2%29 Divide both sides by -2 to isolate t (note: Remember, dividing both sides by a negative number flips the inequality sign)



t%3C1%2F2 Reduce

--------------------------------------------------------------
Answer:
So our answer is t%3C1%2F2 (which is approximately t%3C0.5 in decimal form)




So the answer in interval notation is


And here's the graph of t%3C1%2F2


Graph of t%3C1%2F2 with the shaded region in blue

note: at the point t=1%2F2, there is an open circle. This means the point t=1%2F2 is excluded from the solution set.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F6+-+1%2F3t+%3E+0
+1%2F6+%3E+1%2F3t+
3t+%3E+6
t+%3E+6%2F3
t+%3E+2……………….interval: [2,infinity%29)
draw dashed line, and shade evrithing above the line
Solved by pluggable solver: PLOT any graph
Graphing function y%3E2:

graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+y%3E2+%29