Solving Inequalities by Addition and Subtraction

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Presentation transcript:

Solving Inequalities by Addition and Subtraction Algebra 1 Notes Lesson 6-1 Solving Inequalities by Addition and Subtraction

Mathematics Standards Number, Number Sense and Operations: Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. Patterns, Functions and Algebra: Generalize patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations. Patterns, Functions and Algebra: Add, subtract, multiply and divide monomials and polynomials. Patterns, Functions and Algebra: Write and use equivalent forms of equations and inequalities in problem situations.

Addition Property of Inequalities For all numbers a, b, and c, the following are true: 1. If a > b, then a + c > b + c. 2. If a < b, then a + c < b + c.

Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9 + 9 + 9 21 ≥ y

Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9 + 9 + 9 21 ≥ y or y ≤ 21

Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9 + 9 + 9 21 ≥ y or y ≤ 21 {y | y ≤ 21}

{y | y ≤ 21} Set builder notation | reads “such that”

Example 1 Solve 12 ≥ y – 9. Then graph it on a number line. 12 ≥ y – 9 + 9 + 9 21 ≥ y or y ≤ 21 {y | y ≤ 21} 17 18 19 20 21 22 23 24 25 26

Subtraction Property of Inequalities For all numbers a, b, and c, the following are true: 1. If a > b, then a – c > b – c. 2. If a < b, then a – c < b – c.

Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line.

Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line. -4 ≤ n or {n | n ≥ -4}

Example 2 Solve 12n – 4 ≤ 13n. Then graph it on a number line. -4 ≤ n or {n | n ≥ -4} -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1

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> < > < Is less than Is at most is fewer than > < > < Is less than Is at most is fewer than Is no less than Is greater than Is more than or equal to Is at least Is greater than Is less than or equal to Is no more than

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Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy.

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) +

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) +

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x <

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5 2 + 1.50 + x < 5

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5 2 + 1.50 + x < 5 3.50 + x < 5

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5 2 + 1.50 + x < 5 3.50 + x < 5 - 3.50 - 3.50

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5 x < 1.50 2 + 1.50 + x < 5 3.50 + x < 5 - 3.50 - 3.50

Write an inequality and solve I only have $5.00 to spend at the candy store. I want to buy two suckers, 3 chocolates and a sugar stick. A sucker costs $1.00, and chocolates cost 50 cents each. Write an inequality to determine if I can buy all of the candy I would like to buy. 2(1) + 3(0.50) + x < 5 x < 1.50 2 + 1.50 + x < 5 Only if the sugar stick 3.50 + x < 5 is at most $1.50 - 3.50 - 3.50

Example 3 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than six times that number minus two. 7n

Example 3 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than six times that number minus two. 7n >

Example 3 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than six times that number minus two. 7n > 6n

Example 3 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than six times that number minus two. 7n > 6n – 2 -6n -6n n > -2

Example 3 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than six times that number minus two. 7n > 6n – 2 -6n -6n n > -2 {n | n > -2}

Example 4 5x + 7 > 6

Example 4 5x + 7 > 6 - 7 -7

Example 4 5x + 7 > 6 - 7 -7 5x > -1

Example 4 5x + 7 > 6 - 7 -7 5x > -1 5 5

Example 4 5x + 7 > 6 - 7 -7 5x > -1 5 5 x > -⅕

Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 - 7 -7 5x > -1 5 5 x > -⅕

Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 x > -⅕

Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 x > -⅕

Example 4 5x + 7 > 6 {x | x > -⅕} - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 - 7 -7 5x > -1 5 5 -⅖ -⅕ 0 x > -⅕

Homework Pg 321 14-50 Evens Omit 38 Use Set Builder AND Number Lines