INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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 0 answersPost by Catherine MOLAKAL on July 31, 2016You are really confusing

### Equations with Absolute Value

• The absolute value of a number is its distance from zero on the number line.
• The absolute value of x is written as |x|. It is always 0 or positive.
• If |x| = a, the either x = a or x = -a. To solve an absolute value equation, solve both of these equations. The solution of the absolute value equation consists of all solutions to each of these equations.
• An absolute value equation can have no solution.
• The graph of the absolute value function has the shape of the letter V. The graph can be translated vertically or horizontally depending on the constants involved in the function.

### Equations with Absolute Value

| 4x − 10 | = 12
• 4x − 10 = 124x − 10 = − 12
• 4x − 10 = 12
• 4x = 22
• x = [22/4]
• x = 4[2/4] = 4[1/2]
• 4x − 10 = − 12
• 4x = − 2
• x = − [2/4]
x = − [1/2]
| 6x − 13 | = 11
• 6x − 13 = 116x − 13 = − 11
• 6x − 13 = 116x = 24x = 4
• 6x − 13 = − 116x = 2x = [1/3]
x = 4 or x = [1/3]
| 8k + 6 | = 24
• 8k + 6 = 248k + 6 = − 24
• 8k + 6 = 24
• 8k = 18
• k = [18/8] = [9/4] = 2[1/4]
• 8k + 6 = − 24
• 8k = − 30
• k = − [30/8] = − [15/4] = − 3[3/4]
k = 2[1/4] or − 3[3/4]
|− 4t − 10 | = 6
• − 4t − 10 = 6− 4t − 10 = − 6
• − 4t − 10 = 6
• − 4t = 16
• t = − 4
• − 4t − 10 = − 6
• − 4t = 4
• t = − 1
t = − 4 or t = − 1
|− 2g − 8 | = 22
• − 2g − 8 = 22− 2g − 8 = − 22
• − 2g = 30
• g = − 15
• − 2g − 8 = − 22
• − 2g = − 14
g = 7
|− 3j + 15 | = 9
• − 3j + 15 = 9− 3j + 15 = − 9
• − 3j = − 6
• j = 2
• − 3j + 15 = − 9
• − 3j = − 24
• j = 8
j = 2 or j = 8
|− v + 5 | = 6
• − v + 5 = 6− v + 5 = − 6
• − v + 5 = 6
• − v = 1
• v = − 1
• − v + 5 = − 6
• − v = − 11
• v = 11
v = − 1 or v = 11
Graph the function
y = |x| − 3
• Make a table of points
•  x
 line
 0
 − 1
 1
 − 3
 3
 − 5
 5
 y
 line
 − 3
 − 2
 − 2
 0
 0
 2
 2
• Graph utilizing the coordinate points
Graph the function
y = | − x + 3| + 1
• Make a table of points
•  x
 line
 0
 1
 3
 5
 7
 9
 11
 y
 line
 4
 3
 1
 3
 5
 7
 9
• Graph utilizing the coordinate points
Graph the function
y = − |[x/2] + 1|
• Make a table of points
•  x
 line
 0
 2
 − 2
 4
 − 4
 − 6
 6
 y
 line
 − 1
 − 2
 0
 − 3
 1
 2
 − 4
• Graph utilizing the coordinate points

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Equations with Absolute Value

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Absolute Value 0:06
• Number Line
• Example
• Absolute Value is N
• Absolute Value Function 3:17
• Example
• g(x) and f(x)
• Solving Absolute Value Equations 6:23
• Absolute Value in Words
• Split Into Two Parts
• Solve Both Equations
• Example 1: Solve the Absolute Value 10:34
• Example 2: Solve the Absolute Value 13:09
• Example 3: Solve the Absolute Value 14:52
• Example 4: Solve the Absolute Value 20:23