SOLUTION: I am trying to help my daughter with her summer math problems before entering 9th grade next school year. Can you help? x + 4 ≥ 5 + 2x ≥ 6 another problem that ha

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Question 49155: I am trying to help my daughter with her summer math problems before entering 9th grade next school year. Can you help?
x + 4 ≥ 5 + 2x ≥ 6
another problem that has me stumped:
5x > 10 + x + 1 > 6
Found 2 solutions by venugopalramana, atif.muhammad:
Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!
I am trying to help my daughter with her summer math problems before entering 9th grade next school year. Can you help?
x + 4 ≥ 5 + 2x ≥ 6
TAKE THE INEQUALITIES ONE BY ONE
X+4>=5+2X
X-2X>=5-4=1
-X>=1
1<=-X......WHEN SIDES ARE INTERCHANGED INEQUALITY GETS REVERSED.(4>3..BUT...3<4)
-1>=X......I...WHEN MULTIPLED WITH -1 INEQUALITY GETS REVERSED.(4>3..BUT..-4<-3)
----------
5+2X>=6
2X>=6-5=1
X>=1/2=0.5
-----------------
NOW COMBINE BOTH ANSWERS
-1>=X>=0.5..THAT IS X LIES BETWEEN -1 AND 0.5
another problem that has me stumped:
5x > 10 + x + 1 > 6
5X>11+X
5X-X>11
4X>11......X>11/4..............I
--------
11+X>6
X>6-11=-5
X>-5........................II
------------------------
COMBINING
X SHOULD BE GREATER THAN -5 AS WELL AS 11/4.THAT IS X SHOULD BE GREATER THAN 11/4
HENCE ANSWER IS X>11/4
Answer by atif.muhammad(135)   (Show Source): You can put this solution on YOUR website!
x + 4 ? 5 + 2x ? 6 

The key to these inequalities is to consider them separately.

1.
x + 4 ? 5 + 2x       AND    5 + 2x ? 6 

  -x ? 1                 AND      2x ?1

x ? -1                  AND       x ?0.5

     
2.
5x > 10 + x + 1 > 6

5x > 11 + x > 6

Again, consider them separately:

5x > 11 + x           AND      11 + x > 6

4x > 11                AND       x > -5

 x > 2.25            AND         x > -5

The answer is x>-5 because it also includes all numbers x>2.25. So we ignore x>2.25 and take x>-5 as our answer.

Hope that helps!

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