~ Chapter 3 ~ Algebra I Algebra I Solving Inequalities

Name: ~ Chapter 3 ~ Algebra I Algebra I Solving Inequalities
Uploaded: 2017-08-15T02:45:15+00:00
Duration: PTM18S18
Channel: Frederick Lucas
Description: ~ Chapter 3 ~ Algebra I Algebra I Solving Inequalities

~ Chapter 3 ~ Algebra I Algebra I Solving Inequalities
Lesson Inequalities & Their Graph Lesson Solving Inequalities Using Addition & Subtraction Lesson Solving Inequalities Using Mult. & Div. Lesson Solving Multi-Step Inequalities Lesson Compound Inequalities Lesson Absolute Value Equations & Inequalities Chapter Review

Inequalities & Their Graph
Lesson 3-1 Inequalities & Their Graph Cumulative Review Chap. 1-2

Lesson 3-1 Inequalities & Their Graph Extra Practice - Chap 2

Lesson 3-1 Extra Practice - Chap 2

Lesson 3-1 Inequalities & Their Graph Notes Inequality – mathematical sentence that contains >, <, ≥, ≤, ≠. Solution of an inequality – any number that makes the inequality true. Example ~ y > 5 Would 6 make the inequality true? What about 7, 4, 9, 22, -5? Graphing solutions of Inequalities Graph y < 3 Graph x > -1 Graph a ≤ -2 Graph -6 ≤ g

Lesson 3-1 Inequalities & Their Graph Notes Graph ½ ≥ c Writing Inequalities to Describe Graphs… Define a variable and write an inequality A bus can seat at most 48 students You must be at least 16 years old to obtain a driver’s license Homework – Practice 3-1

Solving Inequalities Using Addition & Subtraction
Lesson 3-2 Practice 3-1

Lesson 3-2 Notes Equivalent Inequalities – Inequalities with the same solution. Ex ~ x > 2 and x – 5 > -3 Steps for solving an inequality (1) Divide the equation at the inequality sign into two equal sides (2) Underline the variable. (3) Identify the number on the same side as the variable. (4) Identify the operation (addition or subtraction) and perform the opposite (inverse operation) to both sides of the equation. (5) Simplify and solve the inequality (6) Check your answer. x + 7 > 22 m – 5 < -61 x > m < -56 Graph the solutions

Lesson 3-2 Notes -3.3 ≤ x t - 5 ≥ 11 -10.8 ≤ x t ≥ 16 Graph the solutions Homework – Practice 3-2 # 1-20

Lesson 3-2 Notes Write & Solve the Inequality that models each situation. Your baseball team has a goal to collect at least 160 blankets for a shelter. Team members brought 42 blankets on Monday and 65 blankets on Wednesday. How many blankets must the team donate on Friday to make or exceed their goal? Your brother has $2000 saved for a vacation. His airplane ticket is $637. How much can he spend for everything else? Homework – Practice 3-2 #21-42

Solving Inequalities Using Mult. & Div.

Lesson 3-3 Notes Steps for solving an inequality (1) Divide the equation at the inequality sign into two equal sides (2) Identify the variable. (3) Identify the number on the same side as the variable. (4) Identify the operation (multiplication or division) and perform the opposite (inverse operation) to both sides of the inequality. (5) Simplify and solve the inequality (If you multiply or divide each side of an inequality by a negative number, you reverse the inequality symbol. ) (6) Check your answer. 11x > m/5 < -6 ÷ ÷ x5 x5 x > m < -30 Graph the solutions

Lesson 3-3 Notes -¾ b ≤ ≤ -0.9 p x(-4/3) x(-4/3) ÷(-0.9) ÷(-0.9) b ≥ ≥ p (another way to solve?) Graph the solution Write & Solve the Inequality that models each situation. Students in the school band are selling calendars. They earn $0.40 on each calendar they sell. Their goal is to earn more than $327. Write and solve an inequality to find the fewest number of calendars they can sell and still reach their goal. Suppose you earn $8.15 per hour working part time at the dry cleaner. Write and solve an inequality to find how many full hours you must work to earn at least $100. Homework ~ Practice 3-3 odd

Solving Multi-Step Inequalities

Lesson 3-4 Notes 3-4 Solving inequalities with variables on one side -3x -4 ≤ < 7 – 2t -3x ≤ < -2t ÷ (-3) ÷(-3)(reverse) ÷(-2) ÷(-2) (reverse) x ≥ > t or t < 1 Now you solve some… -8 < 5n – – 5k ≤ 2 3 < n k ≥ 2 Distributive Property & Inequalities 4p + 2(p + 7) < ≤ 5 – 2(4m + 7) 4p + 2p + 14 < ≤ 5 – 8 m – 14 6p + 14 < ≤ -8m - 9 Then… Solve like other multi step inequality

Notes Lesson 3-4 Solving inequalities with variables on both sides 6z – 15 < 4z (4 – m) ≥ 4(2m + 1) z < m ≤ 8/11 Your turn… 3b + 12 > 27 – 2b -6(x – 4) ≥ 7(2x – 3) b > ≥ x or 2 ¼ ≥ x Write & Solve an inequality One half the difference of t and six is less than or equal to four ½(t – 6) ≤ 4 The perimeter of an isosceles triangle is at most 27 cm. One side is 8 cm long. Find the possible length of the two congruent sides. Homework Practice 3-4 odd

Compound Inequalities

Lesson 3-5 Notes Compound Inequalities – Two inequalities joined by the word and or or. For example x > -6 and x < 8… How could we write this? -6 < x < 8 Graph? The solution for “and” joined inequalities is the overlap of the two graphs… i.e. where both graphs show the same solutions. Write and graph the compound inequalitity All real numbers greater than -2 but less than 9 -2 < x < 9 The books were priced between $3.50 and $6.00, inclusive. 3.50 ≤ c ≤ 6.00 Solving a compound inequality containing and… Solve each inequality… then simplify -6 ≤ 3x < solve ≤ 3x and x < 15 -2 ≤ x x < 5

Lesson 3-5 Notes 7 < -3n + 1 ≤ Solve & Graph… 7 < -3n and n + 1 ≤ Solution: -2 > n and n ≥ -4 or -4 ≤ n < -2 Writing compound Inequalities with or Discounted fares are available to children 12 and under or to adults at least 60 years of age. a ≤ 12 or a ≥ 60 Graph the solution… What else do we know? Write an inequality that represents all real numbers that are at most -5 or at least 3. Graph your solution. Solving a compound inequality containing or -2x + 7 > 3 or 3x – 4 ≥ 5 Graph the solution x < or x ≥ 3 Homework Practice 3-5 odd

Absolute Value Equations & Inequalities

Lesson 3-6 Notes Absolute Value – distance a number is away from 0. Solving an absolute value equation |x| + 5 = 11 |t| - 2 = -1 |x| = |t| = 1 x = 6 & x = t = 1 & t = -1 3|n| = = 3|w| - 2 |n| = = |w| n = 5 & n = w = 2 & w = -2 More absolute value equations Sometimes an absolute value equation has the expression inside the absolute value symbols. Solving Absolute Value Equations ~ To solve an equation in the form |A| = b, where A represents a variable expression and b > 0, solve A = b and A = -b.

Lesson 3-6 Notes |c - 2| = 6 this means… c - 2 = 6 or c - 2 = Why? Solve … c = c = -4 Your turn… -5.5 = |r + 2| |y - 3| = 9

Lesson 3-6 Notes Solving Absolute Value Inequalities |n - 2| < 5 (represents all numbers whose distance from 2 is less than 5 units) So… -5 < n - 2 < 5 Graph the solution |n - 2| > 5 (represents all numbers whose distance from 2 is more than 5 units) So… n – 2 < -5 or n-2 > Graph the solution Here are the rules… Rule 1 ~ To solve an inequality in the form |A| < b, where A is a variable expression and b > 0, solve –b < A < b. Rule 2 ~ To solve an inequality in form |A| > b, where A is a variable expression and b > 0, solve A < -b or A > b. Similar rules are true for |A| ≤ b or |A| ≥ b.

Lesson 3-6 Notes Solve & graph the solutions… |v - 3| ≥ 4 Rule 1 or 2? v – 3 ≤ or v – 3 ≥ 4 v ≤ v ≥ 7 Solve & graph the solutions… |w + 2| < 5 Rule 1 or 2? -5 < w + 2 < < w and w + 2 < 5 -7 < w and w < 3 … < w < graph… Write an absolute value inequality and solve All numbers less than 3 units from 0 |n| < 3 The ideal diameter of a gear for a certain type of clock is mm. An actual diameter can vary by 0.06 mm. Find the range of acceptable diameters. |d – 12.24| ≤ Rule 1 or 2? -0.06 ≤ d – ≤ 0.06 Homework ~ Practice 3-6 #1-28 even & 29-36

~ Chapter 3 ~ Algebra I Algebra I Chapter Review

~ Chapter 3 ~ Algebra I Algebra I Solving Inequalities

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