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Solve for x.1. 6(2x – 3) – 2(6x + 1) = 10x
2. 15 + 2x – 4 = 9x + 11 – 7x
Solve for h. 3.
Warm – up #4
1. 6(2x – 3) – 2(6x + 1) = 10x12x – 18 – 12x – 2 = 10x - 20 = 10x
10 10x = –2
Warm – up #4 Solutions
2. 15 + 2x – 4 = 9x + 11 – 7x 11 + 2x = 11 + 2x
-11 -11 2x = 2x
-2x - 2x0 = 0
ALWAYS TRUE!!! Infinite
Solution!!
Warm – up #4 Solutions
3. Solve for h.
Warm – up #4 Solutions
Lesson 1 – 5 Solving Inequalities Day 1
Algebra II
To solve & graph inequalities
To write & solve compound inequalities
Learning Objective
Open circle on the number lineDoes NOT include the #
> Greater than< Less than
Closed circle on the number lineINCLUDES the #
Greater than or equal toLess than or equal to
x > 7 x is greater than 7
x 7 x is greater than or equal to 7
Writing & Graphing Inequalities
x < 7 x is less than 7
x 7 x is less than or equal to 7
Writing & Graphing Inequalities
Inequalities Words
Less Than < Less Than or Equal to Is fewer than
Is less than Is at most Is no more than
Is at maximum
Inequalities WordsGreater Than > Greater Than or
Equal to Is more than Is larger than Is at least
Is no less than Is at minimum
5 fewer than a number is at least 12
x – 5 12
The quotient of a number and 3 is no more than 15
Write an Inequality from a Sentence
ALWAYS FLIP THE
INEQUALITY SIGN
WHEN YOU
DIVIDE BY – #
1. -3(2x – 5) + 1 4-6x + 15 + 1 4 -6x + 16 4 - 16 - 16 -6x - 12
-6 - 6 x 2
Solve & Graph Inequalities
FLIP!!!
2. -2(x + 9) + 5 < 3-2x – 18 + 5 < 3 -2x – 13 < 3 +13 +13 -2x < 16
-2 - 2 x >-8
Solve & Graph Inequalities
FLIP!!!
3. -2(3x + 1) > -6x + 7-6x – 2 > - 6x + 7 +2 +2 -6x > -6x + 9
+6x +6x 0 > 9
NEVER TRUE! No Solution
Solve & Graph Inequalities
4. 5(2x – 3) – 7x < 3x + 810x – 15 – 7x < 3x + 8 3x – 15 < 3x + 8 -3x -3x
- 15 < 8ALWAYS TRUE! Infinite Solutions
Solve & Graph Inequalities
5. 4(2x – 3) > 8(x + 1)8x – 12 > 8x + 8
-8x -8x - 12 > 8
NEVER TRUE! No Solution
Solve & Graph Inequalities
Compound Inequality – join two inequalities with the word and or or
“And” compound inequality – Find all values of the variable that make BOTH inequalities true. Need overlap
“Or” compound inequality – Find all values of the variables that make at least one of the inequalities true
6. 7 < 2x + 1 and 3x 18 -1 -1 & 3 3
6 < 2x & x 6 2 2 3 < x x > 3 and x 6 3 < x 6
Solve & Graph Inequalities
7. 5 3x - 1 and 2x < 12 +1 +1 & 2 2
6 3x & x < 6 3 3 2 x x 2 and x < 6 2 x < 6
Solve & Graph Inequalities
8. 5< x + 1 < 13 -1 -1 - 1
4 < x < 12
Solve & Graph Inequalities
Read: x + 1 is greater than 5 AND less than 13
9. 7 + x 6 or 8 + x < 3 -7 -7 -8 -8
x -1 or x < - 5
NOT -5> x -1 NOR -1 x <- 5
Solve & Graph Inequalities
00
10. 7x + 3 > 11 or 4x – 1 < -13 -3 -3 +1 +1
7x > 8 or 4x < -12 7 7 4 4
x > or x < -3
Solve & Graph Inequalities
00
11. 16 < 5x + 1 or 3x + 9 < 6 -1 -1 -9 -9
15 < 5x or 3x < -3 5 5 3 3
3 < x or x < -1x > 3 or x < -1
Solve & Graph Inequalities
00
Your friend solved the problem as shown.
What was his error?
Ticket Out the Door
Assignment:
Pg. 38 #15 – 23 odd, 45 – 49 odd