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Unit 4 Inequalities. Graphing Inequalities Translating Inequality Words Solving Inequalities Inequality Word Problems. Inequalities. OBJECTIVE: Given five inequalities, the student will be able to solve for the variable and graph the result with 80% accuracy.
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Unit 4 Inequalities • Graphing Inequalities • Translating Inequality Words • Solving Inequalities • Inequality Word Problems
Inequalities OBJECTIVE: Given five inequalities, the student will be able to solve for the variable and graph the result with 80% accuracy. Ca.SS 5.0: Students solve multi-step equations involving linear inequalities.
1. 5y + 8 < -92 2. -7 – 10y 5 – 7y 3. 4. 0.6x – 1.8 1.2 x Check for Understanding
= Inequalities
= NOT Inequalities
Larger # Smaller # Smaller # Larger # Inequalities Greater Than Less Than
≥ Greater than or equal > Greater than ≤ Less than or equal <Less than ≥ -7 -6 -5 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 > ≤ < Graphing Inequalities X ≥ 1 X > 5 X ≤ -3 X < 0
X ≥ 8 -7 -3 -3 The Only Way They Are Different From Regular Equations is… If there is a negative coefficient, then you ; • Treat the inequality exactly the same as you would solve an equation • Then change the direction of the “inequality” on the last step. -3X < -18 (-7) (-7) X > 6 X ≤ -56
8y –4 < -52 +4 +4 8y < -48 8 8 y < -6 15x + 3–14x 7 x + 3 7 -3 -3 x 4 Try These… 8y –4 < -52 15x + 3 –14x 7
6 – 8m> 22 -6 -6 - 8m > 16 -8 -8 m < -2 7 – 8y 5 – 7y +7y +7y 7 – x 5 -7 -7 - x -2 -1 -1 x 2 Try These… 6 – 8m> 22 7 – 8y 5 – 7y
10 – 3x 4 -10 -10 -3x -6 -3 -3 x 2 Try These… 5 3 1 •15 • 15 • 15
0.3x + 5.4 -1.0x + 0.2 Move every decimal over 1 place 3x + 54 -10x + 2 +10x +10x 13x + 54 2 -54 -54 13x -52 13 13 x -4 Try These… 0.3x+5.4 -x+0.2
1. 5y + 8 < -92 2. -7 – 10y 5 – 7y 3. 4. 1.2 x 0.6x – 1.8 Check for Understanding y< -20 y -3 x 1 x -3
Summary Inspiration: • What do the following inequalities mean? > ≤ • What do you do when you multiply or divide by a negative? • How is solving inequalities like solving equations?
Writing Inequalities OBJECTIVE: Given 5 word problems, the student will be able to write the inequality with 80% accuracy. Ca.SS 5.0: Students solve multi-step equations involving linear inequalities.
Check for Understanding • A number is less than 7 • 5 more than a number is at least 3 • 13 less than x is more than 5 • Twice a number m is at most –4 • The number x is at least as great as the number y
You always need to think about $$$ in your pocket The approach… If I have at least 5 dollars in my pocket…
You always need to think about $$$ in your pocket The approach… Then I have 5 dollars or more (greater than or =)
You always need to think about $$$ in your pocket The approach… If I have at most 30 dollars in my pocket Then I have 5 dollars or more (greater than or =)
You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =)
You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) If I have more than 50 dollars…
You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) Then I have $50.01 or more (greater than) If I have less than 17 dollars… By Marianne Ilmanen
You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) Then I have $50.01 or more (greater than) Then I have $16.99 or less (less than) By Marianne Ilmanen
Inequalities in Word Problems A number decreased by negative 4 is at least 9. A numberdecreased by negative 4is at least 9. X – (-4) ≥ 9 X +4≥ 9
At the maximum $9 At most $9 Greater than $9 At the minimum $9 Less than $9 At least $9 No more than $9 No less than $9 X 9 The Amount of Money in your Pocket is…. • X 9 • X 9 X 9 Interpretation Trick • X 9 • X 9 • X 9 X 9
Let’s Try a Few A number “Y” is less than 4
Let’s Try a Few Y < 4 A number “Y” is less than 4
Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½
Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X 2 ½
Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X 2 ½ A number “M” is at least 3
Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X 2 ½ A number “M” is at least 3 M 3 "At least" means equal or more...
Let’s Try a Few A number “P” is at most –4
Let’s Try a Few P -4 A number “P” is at most –4
Let’s Try a Few P -4 A number “P” is at most –4 3 less than a number is at least 10
Let’s Try a Few P -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10
Let’s Try a Few P -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10 6 times a number is greater than - 1
Let’s Try a Few P -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10 6 timesa numberis greater than - 1 6m -1
Let’s Try a Few 13 less than twice a number is at least –6
Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6
Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6 7 more than half of a number is at most 5
Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6 ½ x + 7 5 7 more than half ofa numberis at most 5
Let’s Try a Few 7 more than a number is more than –17
Let’s Try a Few X + 7 -17 7 morethana numberis more than –17
Let’s Try a Few X + 7 -17 7 morethana numberis more than –17 -15 less than “P” cubed is at least 35
Let’s Try a Few X + 7 -17 7 morethana numberis more than –17 -15 less than“P” cubedis at least 35 P3+ 15 35
Check for Understanding X< 7 X + 5 3 • A number is less than 7 • 5 more than a number is at least 3 • 13 less than x is more than 5 • Twice a number m is at most –4 • The number x is at least as great as the number y X – 13 5 2m -4 X Y
Summary Inspiration • Describe the “trick” to interpreting the correct inequality from word problems. • What do inequalities mean? • How do Inequalities apply to your reality?