Solving OneStep Inequalities

1
Solving One-Step Inequalities
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
All real numbers greater than -2
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 in one variable is a
value of the variable that makes the inequality
true.
Equivalent inequalities have the same solutions.
EXAMPLE x ? 5 and 5 ? x are equivalent
inequalities.
5
PROPERTIES OF INEQUALITY
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

8

• 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. 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.
11

• In the previous example, 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.

13

• Multiply by a Positive Number

14

• Divide by a Positive Number

Solve 4x gt 20 Then graph the solution.
15
Solve the inequality. Then graph the solution

• 18 ? 2k

• -21 ? 3y

16
PROPERTIES OF INEQUALITY
Multiplication Property of Inequality (c lt 0) For
all real numbers a, b, and for c lt 0 If a gt b,
then ac lt bc If a lt b, then ac gt bc
Division Property of Inequality (c lt 0) For all
real numbers a, b, and c lt 0 If a gt b, then a
c lt b c If a lt b, then a c gt b c
17

• Multiply by a Negative Number

18

• Divide by a Negative Number

19
Solve the inequality. Then graph the solution

20
Solve the inequality. Then graph the solution

• 12 gt -5n

21
Homework p. 337 22-54 evens, 55-63, 68, 72-82
evens