Download distance - Greer Middle College

Get out your notebooks!
Today’s Objectives:
You will be able to solve absolute
value equations.
Warm Up
Solve the following equations.
1. −2 3𝑥 − 5 − 4 𝑥 + 10 = −50
2. 3 𝑥 − 9 − 2 6𝑥 − 3 = 6
1.4 Solving Absolute Values
Find the distance between the following
two points on the real number line.
-5
-4
-3
-2
-1
0
1
2
3
4
5
1.
2 𝑎𝑛𝑑 − 5
3.
−3 𝑎𝑛𝑑 − 1
2.
−5 𝑎𝑛𝑑 2
4.
1 𝑎𝑛𝑑 − 3
Distance
The distance between two
real numbers is the absolute
value of their ___________.
1.
2 𝑎𝑛𝑑 − 5
3.
−3 𝑎𝑛𝑑 − 1
2.
−5 𝑎𝑛𝑑 2
4.
1 𝑎𝑛𝑑 − 3
Distance Statements
Rewrite the absolute value statements
as distance statements.
1.
3 − 2 is the same as saying “the distance
between ____ and ____.”
2.
5 + 2 is the same as saying “the distance
between ____ and ____.”
Distance Statements
Rewrite the absolute value statements
as distance statements.
1.
𝑥 − 4 is the same as saying “the distance
between ____ and ____.”
2.
𝑥 is the same as saying “the distance
between ____ and ____.”
Distance
Therefore, distances are
always positive because an
absolute value is always
positive.
Scenario
Sarah’s height is "𝒔" inches and Jessica’s
height is "𝒋" 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?
Scenario
Make 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?
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
1.
𝑥−0 =2
words: the distance from 𝑥 to 0 is _____.
-5
-4
-3
-2
-1
0
1
2
3
4
𝒙 =______ or 𝒙 =______
5
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
2.
𝑥 =5
words: _____________________________.
-5
-4
-3
-2
-1
0
1
2
3
4
𝒙 =______ or 𝒙 =______
5
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
3.
𝑥−1 =3
words: _____________________________.
-5
-4
-3
-2
-1
0
1
2
3
4
𝒙 =______ or 𝒙 =______
5
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
4.
1−𝑥 =3
words: _____________________________.
-5
-4
-3
-2
-1
0
1
2
3
4
𝒙 =______ or 𝒙 =______
5
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
5.
𝑥+1 =4
words: _____________________________.
-5
-4
-3
-2
-1
0
1
2
3
4
𝒙 =______ or 𝒙 =______
5
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
6.
𝑥+2 =3
words: _____________________________.
𝒙 =______ or 𝒙 =______
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
7.
𝑥−5 =0
words: _____________________________.
𝒙 =______ or 𝒙 =______
Examples
Write a sentence in words, draw a
graph, and identify the solutions.
8.
𝑥 + 3 = −4
words: _____________________________.
𝒙 =______ or 𝒙 =______
Generalizing
9.
𝑥−𝑏 =𝑐
words: _______________________________.
Which value (𝑏 or 𝑐) is plotted first?_____
Which value tells the difference?_____
𝒙 =______ or 𝒙 =______
Word Problem
Identical vacation cottages, equally spaced
along a street, are numbered
consecutively. Maria lives in cottage #17.
Joshua lives 4 cottages away from Maria. If
𝑛 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.
Examples
10. 2 = 22
2 𝑥 − 6 = 22
𝒙 =______ or 𝒙 =______
Examples
11. 9 + 3 = 12
9 + 3 𝑥 + 8 = 12
𝒙 =______ or 𝒙 =______
Examples
12. 4𝑥 − 2 = 10
4𝑥
𝟒𝒙 =______ or 𝟒𝒙 =______
𝒙 =______ or 𝒙 =______
Examples
13. 200 − 3𝑥 = 896
3𝑥
𝟑𝒙 =______ or 𝟑𝒙 =______
𝒙 =______ or 𝒙 =______
Examples
14.
2𝑥 + 3 = 5
Examples
15.
70 + 5𝑥 = 15
Examples
16. 3 2𝑥 − 3 − 5 = 4
Examples
17. −2 5𝑦 − 1 = −48
Ticket Out The Door
1. Write an absolute value equation
that corresponds to…
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?
2. Draw a visual representation on a
number line, and
3. Solve the equation.
Homework
Lesson 1.4
Pg. 30 #’s 23-24, 27-32