Absolute Value Scribe Post

Today our topic of learning was absolute value.

Absolute Value: The distance from zero on a number line. The absolute value is always positive.

To show a number as absolute value or and equation it goes between two bars.

Ex. 3= 3 or -3= 3

In reverse..

x= 3 or -3 because they are both a distance of 3 from 0 on a number line.

Steps to solve a problem with absolute values;

Step 1: Isolate Absolute Value Expression

Step 2: Split into Two Different Equations

Step 3: Solve Each Equation Seperately

Step 4: Check Both Solutions Note: this is not optional Mrs. Nowak requires it.

Example Equation 1:

2x-4=10

+4 +4

2x=14

divide both sides by 2

x=7

x=7 or x=-7

Check:

2-7-4=10

2(7)-4=10

14-4=10

10=10....Now that I've checked it, the problem can be considered done, however the solution isn't always the right one.

Example 2:
1/2x+4=x

multiply each side by 2

x+4=2x

split the problem into two equations

Problem 1.. x+4=2x Problem 2.. -(x+4)=2x

-x -x -x-4=2x

solution 4=x +x +x

solution -4/3=3x/3

Check problem 1:

1/24+4=4

1/28=4

1/2(8)=4

4=4 solution 1 is correct

Check problem 2:

1/2-4/3 +4=-4/3

1/2 -4/3 + 12/3=-4/3

1/28/3=-4/3

8/6=-4/3 solution 2 is incorrect, that means its an Extraneous Solution and only solution 1 is the correct answer to the problem.