Solving Inequalities Using Addition or Subtraction

1
Solving Inequalities Using Addition or
Subtraction
6.1

• Goal
• Solve and graph one-step inequalities in one
  variable using addition or subtraction.
• Key Words
• graph of an inequality
• equivalent inequalities

2

• Graph an Inequality in One Variable

Write a verbal phrase to describe the inequality.
Then graph the inequality.
INEQUALITY VERBAL PHRASE GRAPH
1. x lt 2
2.
x is greater than -2
3. x ? 1
4.
-3 -2 -1 0 1 2
3
3
Write a verbal phrase to describe the inequality.
Then graph the inequality.

• t gt 1

• x ? -1

• n lt 0

• y ? 4

4
A solution of an inequality is a value of the
variable that makes the inequality true.
Is 4 a solution of the following inequalities? x
gt -3 x lt 0
Equivalent inequalities have the same solutions.
5
PROPERTIES OF INEQUALITIES
Addition Property of Inequality For all real
numbers a, b, and c If a gt b, then a c gt b
c If a lt b, then a c lt b c
Subtraction Property of Inequality For all real
numbers a, b, and c If a gt b, then a - c gt b -
c If a lt b, then a - c lt b - c
6

• Use Subtraction to Solve an Inequality

Solve x 5 ? 3. Then graph the solution.
7
Solve the inequality. Then graph the solution.

• x 4 lt 7

• n 6 ? 2

• 5 gt a 5

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• Use Addition to Solve an Inequality

Solve -2 gt n 4. Then graph the solution.
9
Solve the inequality. Then graph the solution.

• x - 5 ? 2

• p 1 ? -4

• -3 lt y 2

10

• Write and Graph an Inequality in One Variable.

ASTRONOMY A light year is the distance light
travels in a year. 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.
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• Deneb is about 1600 light years from Earth.
  Write an inequality that describes the distances
  (in light years) to points in space that are
  farther from Earth than Deneb is. Then graph the
  inequality.

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Homework pp. 326-7 20-28e, 42-54e, 58, 63,
64 (15 problems)