Section 2 – 6 HW:
Reading and Graphing Inequalities
Selected Worked Homework Problems
Read the variable side first
1.
x < 5!
2.
x is on the large open side
a line is under the inequality sign
x is on the small pointy side
The inequality is read
x is less than 5
−8 ≤ x
The inequality is read
x is greater than or equal to − 8
!
The answer is B
3.
x ≤ −3!
The answer is G
−3 > x
4.
!
x is on the small pointy side
a line is under the inequality sign
x is on the small pointy side
The inequality is read
x is less than − 3
The inequality is read
!
x is less than or equal to − 3
!
The answer is N
The answer is E
!
5.
!
x ≤ −4 !
x is on the small pointy side
a line is under the inequality sign
The inequality is read
!
x is less than or equal to − 4
6.
−8 < x !
x is on the large open side
The inequality is read
x is greater than − 8
The answer is F
The answer is M
Math 100 !
Section 2–6 HW WKD
!
© 2015 Eitel
2 ≥ x!
7.
x > −3!
8.
x is on the small pointy side
a line is under the inequality sign
The inequality is read
!
x is less than or equal to 2
x is on the large open side
The inequality is read
x is greater than − 3
!
The answer is L
The answer is I
16.
x > −9 !
3≤ x
17.
x is on the large open side
The inequality is read
x is greater than − 3
x is on the large open side
a line is under the inequality sign
!
The inequality is read
x is greater than or equal to 3
The answer is C
The answer is G
!
The open circle means
−9 is not a solution
!
but all real numbers to the
right of − 9 are solutions
Math 100 !
The closed circle means
3 is a solution
and all real numbers to the
right of 3 are also solutions
Section 2–6 HW WKD
!
© 2015 Eitel
x < −4 !
18.
−5 ≥ x
19.
x is on the large open side
The inequality is read
x is greater than − 4
x is on the small pointy side
a line is under the inequality sign
The inequality is read
x is less than or equal to − 5
!
The answer is G
G.
The answer is A
A.
!
–4
–5
The open circle means
−4 is not a solution
!
but all real numbers to the
left of − 4 are solutions
x ≤ −9 !
20.
The closed circle means
−5 is a solution
and all real numbers to the
left of − 5 are also solutions
x is on the small pointy side
a line is under the inequality sign
x is on the large open side
The inequality is read
x is greater than − 4
The inequality is read
!
x is less than or equal to − 9
The answer is I
I.
–9
The answer is K
!
The closed circle means
−9 is a solution
!
and all real numbers to the
left of − 9 are also solutions
Math 100 !
−4 < x
21.
K
–4
The open circle means
−4 is not a solution
but all real numbers to the
right of − 4 are solutions
Section 2–6 HW WKD
!
© 2015 Eitel
Graphing Inequalities
Remember that we want to know what numbers will work for x. This means that we do not read
every inequality from left to right. Read each inequality by reading the x term first no matter
which side it is on and then continue reading in the direction needed to complete the sentence.
!
Example 1!
x>4
x is greater than 4
(it's not equal to 4) !
Example 2!
4≤x
x is greater than
or equal to 4 !
4
29.
4
x > 2!
!
2
Math 100 !
4
Example 4
4≥ x
x is less than
or equal to 4
4
30. x ≤ −4 !
!
x is on the small pointy side
a line is under the inequality sign
The inequality x > 2 is read
x is greater than 2
Place an open circle at 2
and shade all real numbers
to the right of 2.
Example 3
x<4
x is less than 4
(it's not equal to 4) !
The inequality is read
x is less than or equal to − 4
Place a closed circle at − 4
and shade all real numbers
to the left of − 4.
!
–4
Section 2–6 HW WKD
!
© 2015 Eitel
31. –2 > x !
32. –1 ≤ x
x is on the small pointy side
x is on the large open side
a line is under the inequality sign
The inequality is read
x is less than − 2
!
Place an open circle at − 2
and shade all real numbers
to the left of − 2.
–2
Math 100 !
The inequality is read
x is greater than or equal to − 1 !
Place an closed circle at − 1
and shade all real numbers
to the right of − 1.
!
–1
Section 2–6 HW WKD
!
© 2015 Eitel