Download Multi-Step Inequalities

Solving Linear Inequalities
6.1-6.3
Verbal Phrase
Inequality
Interval
Notation
35
Graph
All real numbers less
than 2
All real numbers
greater than −2
All real numbers less
than or equal to 1
All real numbers
greater than or equal
to 0
When you just want greater than or less than, you use an
on the graph.
When you want (greater than or equal to) or (less than or equal to), you’ll use
Try these:
1.
x > 3
2.
x < −1
3.
x ≥ 2
4.
x ≤ 0
Graph
Interval Notation
What if an equation is not quite ready to graph? You already know how to get a
variable by itself . . . that is just what you’ll do here!!
Example:
x + 3 < 10
−3 −3
x
< 7
Undo the added 3 by subtracting 3 from both sides
Steps:





Isolate the variable by using the opposite operation
Be sure the variable is on the LEFT hand side of the inequality to graph correctly
< > use OPEN circles
  use CLOSED circles
Shade in the direction of the “arrow”
Try these:
Inequality
1. x  7  12
Solution
2.
9  x 3
3.
4  x   5
4.
x  8  12
Interval Not. Graph
5x > 20
Example:
5x 20

Undo the multiplied 5 by dividing both sides by 5
5
5
x > 4
The only time this gets difficult is if you have to divide both sides or multiply both sides by a
NEGATIVE number!!!
So, when you multiply or divide both sides by a negative number,
just flip the inequality!!
Example −3x > 15
 3x
3
>
15
3
As soon as I divide by the negative number, I circle the
inequality to remind me to change it on the next line!!
x < − 5
Example
x
 2
4
4
x

1
4
x > 8
<
−2(−4)
Try These:
Inequality
1.
 18  9x
2.
x
 12
4
3.
 15x  30
4.  20  
Solution
Interval Not.
Graph
5
x
4
Multi-Step Inequalities
Solving multi-step inequalities is very similar to solving equations with the exception of when to flip
the symbol. Remember to flip the symbol when you ____________________!
Steps to solving inequalities:
 Isolate the variable to the LEFT side of the inequality
 Add or subtract to isolate the variable term
 Multiply or divide to isolate the variable
 Remember to FLIP the symbol when necessary
Try These:
1.
2x  14  4x  4
2. 6x  3  3x  2
4.
2
6x  9  6x  18
3
5.
2
x  8  4
3
3.  2x  4  6x  4
6. 8  23x  4  10x  20
Class Work:
Write your answer in interval notation and graph the answers.
1. x 1  7
2. 42  6x
3. 7  3x  16
4. 2x 10  x 1
5.  x  3  7
6.  2x  3  4x  7
7. 17 x 11  4x  31
8. 3(2 x  9)  4( x  3)
1
2
6.1-6.3 Solving Inequalities Homework
Solve each inequality. Write your answer in interval notation and graph the
answers.
1. 2m + 7 > 17
2. -2 – 3x ≥ 2
3. 7x - 1 < 26 - 2x
4. 2x + 5 < 3x - 7
5.
2x  3
7
5
6. 9r + 15 ≥ 24 + 10r

7. 4y + 2 < 8y – (6y – 10)
8. 5(2h – 6) – 7(h + 7) > 4h
36
9. 3x −5>15−2x
10. 2x−3(1−2x)≤31
11. x ≥1− x
12. 2x <3−4x
13. x ≥2+3x
14. −3x <2
15. 2.3 ≥ −0.2x
16. −2x <1− x