SOLUTION: I have been struggling with this problem for a while now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!!
Combining Open Sen
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Question 126360This question is from textbook Algebra Structure and Method
: I have been struggling with this problem for a while now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!!
Combining Open Sentences
solve each open sentence. Graph the solution set, if there is one.
6-c is less than 2c+3 is less than or equal to 8+c
This question is from textbook Algebra Structure and Method
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
6-c is less than 2c+3 is less than or equal to 8+c
-----------------------------
6-c <= 2c+3
3c>=3
c> -1
----------
AND
----------
2c+3<=8+c
c<=5
------------
Final: -1 < c <=5
=================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given inequality
Break up the inequality. Remember is equivalent to the group and
and
Now let's solve the first inequality
Start with the given inequality
Subtract 6 from both sides
Subtract 2c from both sides
Combine like terms on the left side
Combine like terms on the right side
Divide both sides by -3 to isolate c (note: Remember, dividing both sides by a negative number flips the inequality sign)
Divide
--------------------------------------------------------------
Answer:
So the first part of our answer is
Start with the given inequality
Subtract 3 from both sides
Subtract c from both sides
Combine like terms on the left side
Combine like terms on the right side
--------------------------------------------------------------
Answer:
So the second part of our answer is
--------------------------------------------------
Putting the the two answers together, we get:
and
Also, the two solutions form the compound inequality
So the solution in interval notation is: (1,5]
Now let's graph the solution set
Note: at there is a open circle (which means this point is excluded) and at there is a closed circle (which means this point is included)
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