Get out your notebooks!

You will be able to solve absolute value equations.

Today’s Objectives:

Warm UpSolve the following equations.

1.

2.

1.4 Solving Absolute ValuesFind the distance between the following two points on the real number line.

1.

2.

3.

4.

-5 -4 -3 -2 -1 0 1 2 3 4 5

DistanceThe distance between two real numbers is the absolute value of their ___________.1.

2.

3.

4.

Distance StatementsRewrite the absolute value statements as distance statements.

1. is the same as saying “the distance between ____ and ____.”

2. is the same as saying “the distance between ____ and ____.”

Distance StatementsRewrite the absolute value statements as distance statements.

1. is the same as saying “the distance between ____ and ____.”

2. is the same as saying “the distance between ____ and ____.”

DistanceTherefore, distances are always positive because an absolute value is always positive.

ScenarioSarah’s height is inches and Jessica’s height is inches.

Their father wants to know how many inches separate his two daughters.

Write an equation for this difference in such a way that the result will always be positive no matter which sister is taller.

Copy This Down…Sarah is at mile marker 44. She is 7 miles from her exit. At what mile marker could Sarah’s exit be located?

ScenarioMake a visual representation on a number line of “the distance from mile marker 44 to Sarah’s exit x is 7.”

Expanded solution:

How might we write a mathematical equation for this visual representation?

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.1.

words: the distance from to is _____.

______ or ______

-5 -4 -3 -2 -1 0 1 2 3 4 5

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.2.

words: _____________________________.

______ or ______

-5 -4 -3 -2 -1 0 1 2 3 4 5

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.3.

words: _____________________________.

______ or ______

-5 -4 -3 -2 -1 0 1 2 3 4 5

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.4.

words: _____________________________.

______ or ______

-5 -4 -3 -2 -1 0 1 2 3 4 5

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.5.

words: _____________________________.

______ or ______

-5 -4 -3 -2 -1 0 1 2 3 4 5

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.6.

words: _____________________________.

______ or ______

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.7.

words: _____________________________.

______ or ______

ExamplesWrite a sentence in words, draw a graph, and identify the solutions.8.

words: _____________________________.

______ or ______

Generalizing9.

words: _______________________________.

Which value ( or ) is plotted first?_____ Which value tells the difference?_____

______ or ______

Word ProblemIdentical vacation cottages, equally spaced along a street, are numbered consecutively. Maria lives in cottage #17. Joshua lives 4 cottages away from Maria. If represents Joshua’s cottage number, then write an inequality that expresses this situation. Draw a visual representation on a number line, and solve the inequality.

Examples10.

______ or ______

Examples11.

______ or ______

Examples12.

______ or ______

______ or ______

Examples13.

______ or ______

______ or ______

Examples14.

Examples15.

Examples16.

Examples17.

Ticket Out The Door1. Write an absolute value equation

that corresponds to…

2. Draw a visual representation on a number line, and

3. Solve the equation.

The carnival guesser tried to guess Aiden’s weight, but she was off by 9 pounds. Aiden actually weights 168 lbs. There are two guesses she could have made, what are they?

HomeworkLesson 1.4Pg. 30 #’s 23-24, 27-32