Lesson 3 Menu : Lesson 3 Menu Five-Minute Check (over Lesson 6-2)
Main Ideas
California Standards
Example 1: Multi-Step Inequality
Example 2: Inequality Involving a Negative Coefficient
Example 3: Write and Solve an Inequality
Example 4: Distributive Property
Example 5: Empty Set and All Reals
Lesson 3 MI/Vocab : Lesson 3 MI/Vocab Solve linear inequalities involving more than one operation. Solve linear inequalities involving the Distributive Property.
Lesson 3 CA : Lesson 3 CA Standard 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x – 5) + 4(x – 2) = 12. (Key, CAHSEE)
Standard 5.0 Students solve multi-step problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. (Key, CAHSEE)
Lesson 3 Ex1 : Lesson 3 Ex1 Multi-Step Inequality
Lesson 3 Ex1 : Lesson 3 Ex1 Original inequality Answer: Water is a gas for all temperatures greater than 100°C. Multi-Step Inequality Subtract 32 from each side. Simplify. Simplify.
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B
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D A. c < –268.9°C
B. c > 268.9°C
C. c > –268.9°C
D. c > –484°C
Lesson 3 Ex2 : Lesson 3 Ex2 Inequality Involving a Negative Coefficient Solve 13 – 11d ≥ 79. Answer: The solution set is {d | d ≤ –6} . 13 – 11d ≥ 79 Original inequality
13 – 11d – 13 ≥ 79 – 13 Subtract 13 from each side.
–11d ≥ 66 Simplify. d ≤ –6 Simplify.
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B
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D A. {y | y < –1}
B. {y | y > 1}
C. {y | y > –1}
D. {y | y < 1} Solve –8y + 3 > –5. BrainPOP: Solving Inequalities
Lesson 3 Ex3 : Lesson 3 Ex3 Write and Solve an Inequality Define a variable, write an inequality, and solve the problem below. Check your solution Four times a number plus twelve is less than a number minus three.
Lesson 3 Ex3 : Lesson 3 Ex3 Write and Solve an Inequality 4n + 12 < n – 3 Original inequality Answer: 4n + 12 < n – 3; The solution set is {n | n < –5} . n < –5 Simplify. 4n + 12 – n < n – 3 – n Subtract n from each side.
3n + 12 < –3 Simplify.
3n + 12 – 12 < –3 – 12 Subtract 12 from each side.
3n < –15 Simplify.
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B
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D Write an inequality for the sentence below. Then solve the inequality.6 times a number is greater than 4 times the number minus 2.
Lesson 3 Ex4 : Lesson 3 Ex4 A. Solve 3(–2x + 4) > –12. Answer: The solution set is {x | x < 4} . Distributive Property 3(–2x + 4) > –12 Original inequality
–6x + 12 > –12 Distributive Property
–6x + 12 – 12 > –12 – 12 Subtract 12 from each side.
–6x > –24 Simplify. x < 4 Simplify. Divide each side by –6 and change > to <.
Lesson 3 Ex4 : Lesson 3 Ex4 B. Solve 6c + 3(2 – c) ≥ –2c + 1. Answer: The solution set is {c | c ≥ –1}. Distributive Property 6c + 3(2 – c) ≥ –2c + 1 Original inequality
6c + 6 – 3c ≥ –2c + 1 Distributive Property
3c + 6 ≥ –2c + 1 Combine like terms.
3c + 6 + 2c ≥ –2c + 1 + 2c Add 2c to each side.
5c + 6 ≥ 1 Simplify.
5c + 6 – 6 ≥ 1 – 6 Subtract 6 from each side.
5c ≥ –5 Simplify.
c ≥ –1 Divide each side by 5.
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B
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D A. Solve 2(3x – 5) > – 20. A. x > –2
B. x < –2
C. x > 2
D. x < 2
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D B. Solve 3p – 2(p – 4) < p – (2 – 3p). Interactive Lab: Solving Linear Equalities
Lesson 3 Ex5 : Lesson 3 Ex5 A. Solve –7(s + 4) + 11s ≥ 8s – 2(2s + 1). –7(s + 4) + 11s ≥ 8s – 2(2s + 1) Original inequality
–7s – 28 + 11s ≥ 8s – 4s – 2 Distributive Property
4s – 28 ≥ 4s – 2 Combine like terms.
4s – 28 – 4s ≥ 4s – 2 – 4s Subtract 4s from each side.
– 28 ≥ – 2 Simplify. Answer: Since the inequality results in a false statement, the solution set is the empty set Ø. Empty Set and All Reals
Lesson 3 Ex5 : Lesson 3 Ex5 B. Solve 4d – 3 > 2d + 3(d + 3) – (d + 12). 4d – 3 > 2d + 3(d + 3) – (d + 12) Original inequality
4d – 3 > 2d + 3d + 9 – d – 12 Distributive Property
4d – 3 > 4d + –3 Combine like terms.
4d > 4d Add 3 to both sides.
d > d Divide each side by 4. Answer: Since the inequality is always true, the solution set is {d | d is a real number}. Empty Set and All Reals
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D A. Solve 8a + 5 ≤ 6a + 3(a + 4) – (a + 7).
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D B. Solve 4r – 2(3 + r) < 7r – (8 + 5r).
End of Lesson 3 : End of Lesson 3