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.

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) (Show Source): You can put this solution on YOUR website!

Start with the given compound inequality.

Break up the compound inequality to get:

AND

So let's solve the first inequality

Start with the given inequality.

Add to both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number.

Reduce.

Now let's solve the second inequality

Start with the given inequality.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is and .

Our answer also looks like .

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 which means that we're including this value in the solution set
Also, there is a closed circle at which means that we're including this value in the solution set.

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