SOLUTION: I need help solving. Thank you x^2 - 8x <= -15

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Question 888525: I need help solving. Thank you
x^2 - 8x <= -15

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!


Get 0 on the right, everything else on the left:





The critical numbers are the numbers which either make
the left side 0 or undefined.

The critical numbers are 3 and 5.

Place these numbers on a number line:

----------------o-----o------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

we test any value less than 3, say 0, in the inequality






That's false so we do not shade the number line to the
left of 3

----------------o-----o------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

we test any value between 3 and 5, say 4, in the inequality






That's true so we shade the number line between 3 and 5.

----------------o=====o------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

we test any value to the right of 5, say 6, in the inequality






That's false so we do not shade the number line to the right of 5.

Next we test the critical points themselves:

----------------o=====o------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

Test 3






That's true so we darken the circle at 3:

----------------●=====o------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

Test 3






----------------●=====●------------  
-2 -1  0  1  2  3  4  5  6  7  8  9

That's true so we darken the circle at 5 also.

The interval notation for the solution is [3,5]

The set builder notation is   

Edwin

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