SOLUTION: Given x-1(less then or equal to)3x + 1(less than or equal to) x + 5. Solve for x and show your answer on the number line and in interval notaion.

Algebra ->  Inequalities -> SOLUTION: Given x-1(less then or equal to)3x + 1(less than or equal to) x + 5. Solve for x and show your answer on the number line and in interval notaion.       Log On


   

Question 168704: Given x-1(less then or equal to)3x + 1(less than or equal to) x + 5. Solve for x and show your answer on the number line and in interval notaion.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x-1%3C=3x%2B1%3C=x%2B5 Start with the given compound inequality.


Break up the compound inequality to get:


x-1%3C=3x%2B1 AND 3x%2B1%3C=x%2B5


So let's solve the first inequality x-1%3C=3x%2B1


x-1%3C=3x%2B1 Start with the given inequality.


x%3C=3x%2B1%2B1 Add 1 to both sides.


x-3x%3C=1%2B1 Subtract 3x from both sides.


-2x%3C=1%2B1 Combine like terms on the left side.


-2x%3C=2 Combine like terms on the right side.


x%3E=%282%29%2F%28-2%29 Divide both sides by -2 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E=-1 Reduce.


Now let's solve the second inequality 3x%2B1%3C=x%2B5


3x%2B1%3C=x%2B5 Start with the given inequality.


3x%3C=x%2B5-1 Subtract 1 from both sides.


3x-x%3C=5-1 Subtract x from both sides.


2x%3C=5-1 Combine like terms on the left side.


2x%3C=4 Combine like terms on the right side.


x%3C=%284%29%2F%282%29 Divide both sides by 2 to isolate x.


x%3C=2 Reduce.

-------------------------------------------------------------------------
Answer:

So the solution is x%3E=-1 and x%3C=2.


Our answer also looks like -1%3C=x%3C=2.





So the answer in interval notation is []


Also, the answer in set-builder notation is


Here's the graph of the solution set

Graph of the solution set

Note:
There is a closed circle at x=-1 which means that we're including this value in the solution set
Also, there is a closed circle at x=2 which means that we're including this value in the solution set.