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EXAMPLE
3
Use Addition to Solve an Inequality
Solve 2 > n 4. Then graph the solution.
Student Help
WRITING ALGEBRA
The inequality 2 > n
can also be written
as n < 2 and has the
same solution as n < 2.
Solution
2 > n 4
Write original inequality.
2 4 > n 4 4
Add 4 to each side.
(Addition Property of Inequality)
2>n
ANSWER 䊳
Simplify.
The solution is all real numbers less than 2. Check the solution.
The graph of the solution is shown below.
3
2
1
1
0
2
3
Use Addition to Solve an Inequality
Solve the inequality. Then graph the solution.
8. x 5 ≥ 2
EXAMPLE
Science
9. p 1 ≤ 4
4
10. 3 < y 2
Write and Graph an Inequality in One Variable
A light year is the distance light travels in a year. One light
year is about 6,000,000,000,000 miles. The star Sirius is about 8.8 light years
from Earth. Write an inequality that describes distances to points in space that
are farther from Earth than Sirius is. Then graph the inequality.
ASTRONOMY
ORION
Solution Let d be the distance in light years of any point in space that is
farther from Earth than Sirius is.
Sirius
The distance is greater than 8.8.
Write the inequality in words:
d > 8.8
Translate into mathematical symbols:
ASTRONOMY You can use
the constellation Orion to
locate Sirius. Orion’s belt
points southwest to Sirius.
ANSWER 䊳
The inequality is d > 8.8. The graph of the inequality is shown below.
8.8
5
6
7
8
9
10
11
Write and Graph an Inequality in One Variable
11. In Example 4, suppose that d represented distances to points in space whose
distance from Earth is greater than or equal to the distance from Earth to
Sirius. How would the inequality change? How would the graph change?
12. Deneb is about 1600 light years from Earth. Write an inequality that
describes the distances to points in space that are farther from Earth than
Deneb is. Then graph the inequality.
6.1
Solving Inequalities Using Addition or Subtraction
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