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Graphing InequalitiesEXAMPLE 1
Inequality Graph Verbal Phrase
a. y < 7
b. q 3
c. x > –5
d. h 212
All numbers less than 7
All numbers less than or equal to 3
All numbers greater than –5
All numbers greater than or equal to 2 1
2
Solving InequalitiesEXAMPLE 2
Solve the inequality. Then graph its solution.
x – 5 + 5 < 8 + 5
x < 13
Original inequality
Add 5 to each side.
Simplify.
x – 5 < 8
a. x – 5 < 8
Solving InequalitiesEXAMPLE 2
y – 7 –10
y – 7 + 7 – 10 + 7
y –3
Original inequality
Add 7 to each side.
Simplify.
b. y – 7 –10
Solving InequalitiesEXAMPLE 2
8 + m > 15
8 – 8 + m > 15 – 8
m > 7
Original inequality
Subtract 8 from each side.
Simplify.
c. 8 + m > 15
GUIDED PRACTICE for Examples 1 and 2
Graph and write a verbal phrase for the inequality.
1. z ≥ –1
SOLUTION
Inequality Graph Verbal Phrase
z ≥ –1 All numbers greater than or equal to –1–3 –2 –1 0 1
GUIDED PRACTICE for Examples 1 and 2
2. 4 > p
SOLUTION
Inequality Graph Verbal Phrase
4 > p All numbers less than 4. 2 3 4 5 6
GUIDED PRACTICE for Examples 1 and 2
3. k –3.5
SOLUTION
Inequality Graph Verbal Phrase
k –3.5 All numbers less than or equal to –3.5.
–5 –4 –3 –2 –1
GUIDED PRACTICE for Examples 1 and 2
4. m > 12
SOLUTION
Inequality Graph Verbal Phrase
12m > All numbers greater than .1
2–2 –1 0 1 2
GUIDED PRACTICE for Examples 1 and 2
5. x – 3 > –2
SOLUTION
Original inequality
Add 3 to each side.
Simplify.
x – 3 > – 2
x – 3 + 3> – 2+ 3
x > 1
Graph
GUIDED PRACTICE for Examples 1 and 2
6. 6 > t – 1
SOLUTION
Original inequality
Add 1 to each side.
Simplify.
6 > t – 1
6 + 1> t – 1+ 1
7 > t
Graph
GUIDED PRACTICE for Examples 1 and 2
7. 12 ≥ p + 14
SOLUTION
Original inequality
Subtract 14 from each side.
Simplify.
12 ≥ p + 14
– 14 ≥ p + 1412 – 14
≥ p–2
Graph
GUIDED PRACTICE for Examples 1 and 2
8. x + 5 < 10
SOLUTION
Original inequality
Subtract 5 from each side.
Simplify.
x + 5 < 10
x + 5 < 10– 5 –5x < 5
Graph x < 53 4 5 6 7
GUIDED PRACTICE for Examples 1 and 2
9. t + 9 6
SOLUTION
Original inequality
Subtract 9 from each side.
Simplify.
t + 9 6
t + 9 – 9 6 – 9
–3t
Graph
GUIDED PRACTICE for Examples 1 and 2
10. –4 < k –3
SOLUTION
Original inequality
Add 3 to each side.
Simplify.
–4 < k – 3
< k – 3 + 3–4 + 3< k–1
Graph