absolute value Equations Unit 1 Day 7 and Inequalities

KEY CONTENT: I can solve a real-life problem by writing and solving an appropriate linear equation and inequality. I can graph a linear function using various graphing methods. Refresher: https://www.youtube.com/wa tch?v=wuVQPkq7Gwc

Guided practice u1a7 Example 1

Guided practice u1a7 Example 1 -15 11

individual practice u1a7 Example 2

individual practice u1a7 Example 2 -22 8

Guided practice u1a7 Example 3

Guided practice u1a7 Example 3

individual practice u1a7 Example 4

individual practice u1a7 Example 4

guided practice u1a7 Example 5

guided practice u1a7 Example 5 The absolute value of a number is always positive or zero, an equation like 𝑥 =−4 is never true. Thus, this absolute value has no solution. The solution set for this type of equation is the empty set, symbolized by { } or Ø.

guided practice u1a7 example 6

guided practice u1a7 example 6 WHY IS THIS AN EXTRANEOUS SOLUTION?

individual practice u1a7 example 7

individual practice u1a7 example 7

guided practice u1a7 example 8 Martin is cutting ribbons for a craft project. Each ribbon needs to be 3/4 yard long. If each piece is always within plus or minus of 1/16 yard, how long are the shortest and longest pieces of ribbon?

guided practice u1a7 example 8 How long are the shortest and longest pieces of ribbon? The shortest pieces of ribbon would be 11/16 yard long and the longest pieces of ribbon would be 13/16 yard long.

guided practice u1a7 example 9 To make cocoa powder, cocoa beans are roasted. The ideal temperature for roasting is 300 0 F, plus or minus 25 0 F. Write and solve an equation describing the maximum and minimum roasting temperature for cocoa beans.

guided practice u1a7 example 9 Describe the maximum and minimum roasting temperature for cocoa beans. The maximum roasting temperature for cocoa beans would be 325 0 F and the minimum roasting temperature for cocoa beans would be 275 0 F.

independent practice u1a7 example 10 Most freshwater tropical fish thrive if the water is within 𝟐 𝟎 F to 𝟕𝟖 𝟎 F. Write an equation to determine the least and greatest optimal temperatures.

independent practice u1a7 example 10

Guided practice u1a7 Example 11 Green plants can live in the ocean only at depths of 0 feet to 80 feet. Write an absolute value inequality describing the range of possible depths for green plants in an ocean.

Guided practice u1a7 Example 11 How an we check this is correct? CORRECT! The depth must be less than or equal to 80 feet. CORRECT! The depth must be greater than or equal 0 feet.

independent practice u1a7 example 12 Ms. Kaufman is planning a trip to Alaska. She purchased a winter coat that is recommended for outdoor temperatures from −𝟏𝟓 𝟎 F to 𝟒𝟓 𝟎 F. Let t represent the temperature for which the coat is intended. Write an absolute value inequality to represent the situation.

independent practice u1a7 example 12 Ms. Kaufman is planning a trip to Alaska. She purchased a winter coat that is recommended for outdoor temperatures from −𝟏𝟓 𝟎 F to 𝟒𝟓 𝟎 F. Let t represent the temperature for which the coat is intended. Write an absolute value inequality to represent the situation.

independent practice u1a7 example 13 The IQ scores for the middle 50% of the population can be written as , where x is the person’s IQ. Solve the inequality to find the interval for the IQ scores for the middle 50% of the population.

independent practice u1a7 example 13 The interval scores for the middle 50% of the population ranges from 90 to 110.

Checking for understanding… Explain what it means for a solution of an equation to be extraneous?

Checking for understanding… Explain what it means for a solution of an equation to be extraneous? A solution to an equation is extraneous if it is a solution to a derived equation, but it is not a solution to the original equation. Simple terms…you correctly solve the problem and arrive at an answer. When you plug your answer back into the original equation, it is does work.

Checking for understanding… When is the absolute value of a number equal to the number itself?

Checking for understanding… When is the absolute value of a number equal to the number itself? When the number has a positive value or is equal to zero.

Checking for understanding… Given an example of a compound inequality that has no solution.

Checking for understanding… Given an example of a compound inequality that has no solution. Answers can vary. Example: x < - 5 and 5x > 25

Checking for understanding… Describe how absolute value equations and inequalities are like linear equations and inequalities and how they differ.

Checking for understanding… Describe how absolute value equations and inequalities are like linear equations and inequalities and how they differ. Answers an vary. Example: An absolute value equation or inequality represent two equations or inequalities. Each equation or inequality is solved in the same manner you solve a linear equation or inequality.