1.7 Solving Inequalities with roots and powers
Square roots with positive numbers
Square both sides:
Solution set:
Square both sides:
Square both sides:
Solution set:
Solution set:
Square roots with negative numbers
If the square root of is greater than a negative
number, then you could plug in any positive
number to for the inequality to be true.
Solution set:
If the square root of is less than a negative
number, then there is no number that you can
plug in to for the inequality to be true, so ther is
no solution
Solution set: No Solution
Squares with positive numbers (you will not have any negative numbers on the other side, only positive numbers)
Square root both sides:
Solution set:
Square root both sides:
Solution set:
Absolute value with negative numbers
If the absolute value of is greater than a negative
number, then all real numbers are the solution
set. You can replace with any real number and
still satisfy the inequality.
If the absolute value of is less than a negative
number, then there are no solutions to the
inequality. There is no number you can replace
with to satisfy the inequality.
Solution set: All real numbers
Solution set: No Solution
Match the following:
1.
a) No solution
2.
b)
3.
c)
4.
d)
5.
e) No solution
6.
f)
7.
g)
8.
h) All real numbers
More information can be found at:
http://www.teachertube.com/viewVideo.php?video_id=3081&title=Graphing_the_Solution_Set_of_an_Inequality_on_a_Number_Line
Answers:
1 – f; 2 – c; 3 – g; 4 – d; 5 – b; 6 – h; 7/8 – a/e