Ch. 3 – Inequalities 
3.1 Linear Inequalities; 
Absolute Value 
Objectives: 
Solve and graph linear inequalities in one va...
Solving Inequalities 
• Solve just like an equation, EXCEPT: 
• The inequality sign must be reversed if you 
multiply or d...
Example 1a 
• Solve 3x – 4  10 + x and graph the 
solution.
Example 1b 
• Solve and graph the solution.
You Try! 
• Solve and graph the 
solution.
Absolute Value 
• |x| means (geometrically) the distance 
from x to zero on the number line. (c  0) 
Sentence Meaning 
Th...
• Sentences with |x – k| can mean the 
distance from x to k on the number line. 
Sentence Meaning Graph Solution 
|x - 5| ...
Algebraic Method 
Sentence Equivalent Sentence 
|ax + b| = c ax + b = c 
|ax + b| < c -c < ax + b < c 
|ax + b| > c ax + ...
Example 2a 
• Solve |3x – 9| > 4 and graph the solution.
Example 2b 
• Solve |2x + 5|  7 and graph the solution.
You Try! 
• Solve and graph the solution: 
• |2x + 3 | = 1 
• |x – 2|  3
Upcoming SlideShare
Loading in …5
×

3 1 linear inequalities, absolute value

574 views

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
574
On SlideShare
0
From Embeds
0
Number of Embeds
46
Actions
Shares
0
Downloads
13
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

3 1 linear inequalities, absolute value

  1. 1. Ch. 3 – Inequalities 3.1 Linear Inequalities; Absolute Value Objectives: Solve and graph linear inequalities in one variable
  2. 2. Solving Inequalities • Solve just like an equation, EXCEPT: • The inequality sign must be reversed if you multiply or divide by a negative number Graphing solutions • On a number line: • < , > use open circle •  ,  use closed circle • Shade (or use an arrow) to indicate solution set.
  3. 3. Example 1a • Solve 3x – 4  10 + x and graph the solution.
  4. 4. Example 1b • Solve and graph the solution.
  5. 5. You Try! • Solve and graph the solution.
  6. 6. Absolute Value • |x| means (geometrically) the distance from x to zero on the number line. (c  0) Sentence Meaning The distance from x to 0 is: Graph Solution |x| = c exactly c units x = c or x = -c -c 0 c |x| < c less than c units -c < x< c |x| > c greater than c units x < -c or x > c -c 0 c -c 0 c
  7. 7. • Sentences with |x – k| can mean the distance from x to k on the number line. Sentence Meaning Graph Solution |x - 5| = 3 The distance from x to 5 is 3 units x = 2 or x = 8 |x - 1| < 2 The distance from x to 1 is less than 2 units -1 < x< 3 |x + 3| > 2 or |x – (-3)| > 2 The distance from x to -3 is greater than 2 units x < -5 or x > -1
  8. 8. Algebraic Method Sentence Equivalent Sentence |ax + b| = c ax + b = c |ax + b| < c -c < ax + b < c |ax + b| > c ax + b < -c or ax + b > c
  9. 9. Example 2a • Solve |3x – 9| > 4 and graph the solution.
  10. 10. Example 2b • Solve |2x + 5|  7 and graph the solution.
  11. 11. You Try! • Solve and graph the solution: • |2x + 3 | = 1 • |x – 2|  3

×