Solving Problems with Absolute Value

Lesson: Solving Absolute Value Equations

by Stephanie Parker

Open Ended

How are you today?

​Sub Reminder

Today we have a guest teacher in our learning lab so I need you to be on your very best behavior.

​

​You have been doing really good and I am EXTREMELY proud of you. Please continue with that even in my absence.

​

​Make sure you are sitting in your seat and doing your work.

​

​I look forward to reading a good sub report! Have a great day!!

​Warm-up: Review Proportions

1. ​Cross Multiply

2. ​Distribute to elminate ( )

3. ​Solve remaining equations

4. ​Make sure solution doesn't make denominator equal to zero.

Multiple Choice

Solve for k

• 165

• 17

• 1/17

• 1/165

Multiple Choice

Solve the proportion

• x = 3

• x = -3

• x = 1

• x = -1

Multiple Choice

Solve for the given variable

• 18

• 3

• 4

• 6

Multiple Choice

Solve the equation for x:

• 17

• 16

• 15

• 14

Multiple Choice

• 5

• -5

• 25

• -25

Poll

How are you feeling about solving proportions?

• 1 - Minimially Proficient

  I have no idea what I am doing.

• 2 - Partially Proficient

  I can cross multiply, but struggle to finish solving.

• 3 - Proficient

  I can cross multiply, distribute and solve.

• 4 - Highly Proficient

  I could teach a friend how to solve a proportion.

​How to solve Absolute Value Equations

1. ​Isolate the Absolute Value

2. ​Create 2 Equations

   1. ​Equation #1: Set "inside" equal to the positive of the other side.

   2. ​Equation #2: Set "inside" equation to the negative of the other side.

3. ​Solve each equation

4. ​Write answer as a solution set

Multiple Choice

$$\left|x-6\right|=3$$  

• $$x=9$$  

• $$x=-9\ or\ x=9$$  

• $$x=9\ or\ x=3$$  

• $$x=-3\ or\ x=3$$  

Multiple Choice

$$\left|x+7\right|=12$$  

• $$x=5\ or\ x=-19$$  

• $$x=5\ or\ x=-5$$  

• $$x=5$$  

• $$x=-5\ or\ x=19$$  

Multiple Choice

∣ 2x + 9 ∣ = 15

• x = 3 

• x = 3 x = -6

• x = 3 x = -12

• x = 6 x = -12

Multiple Choice

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2

Multiple Choice

Solve

$$\left|2x+4\right|=8$$  

• x= 10 or x=-9

• x=2  or x= -6

• x= -4  or  x=6

• x= -2

​Lesson: Isolating the Absolute Value

​Complete your notes using the video below.

Multiple Choice

| 3x - 6 | - 9 = -3

• No Solution

• x = 0 and x = 4

• x = 2 and x = -2

• x = -4 and x = 4

Multiple Choice

|v + 8| − 5 = 2 

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

Multiple Choice

Solve: $$\left|x-12\right|-3=11$$  

• $$x=-2\ \ \ OR\ \ \ x=-26$$  

• $$x=-2\ \ \ OR\ \ \ x\ =\ 26$$  

• $$x=3\ \ \ OR\ \ \ x\ =\ 25$$  

• $$x\ =\ 4\ \ \ OR\ \ \ x\ =\ -7$$  

Multiple Choice

Solve for x: $$-2\left|5x-1\right|-3=-11$$  

• $$x=-\frac{3}{5}\ \ \ OR\ \ \ x\ =\ 1$$  

• $$x=\frac{3}{5}\ \ OR\ \ x\ =\ -1$$  

• $$x=-\frac{2}{3}\ \ OR\ \ x\ =\ 5$$  

• $$x=\frac{2}{3}\ \ \ OR\ \ \ x\ =\ -5$$  

Multiple Choice

Solve the following equation:

3| −8x| + 8 = 80

• {−7/3, 7/3}

• {−3, 3}

• {11/3, −11/3}

• No Solution

Multiple Choice

Solve for x: 2|x + 9| = 8

• x = -5 or x = -13

• x = -13

• x = -1/2 or x = -17/2

• No Solution

Multiple Choice

Solve the equation: $$\left|2x-3\right|+5=10$$  

• {−1, 1}

• {−1, 4}

• {−1, −4}

• {1, 4}

Multiple Choice

Solve the equation: $$9\left|9-2p\right|=81$$  

• $$p=0,\ p=-9$$  

• $$p=-\frac{63}{2},\ p=\frac{99}{2}$$  

• $$p=0,\ p=9$$  

• No Solution

Multiple Choice

Solve the equation: $$8\left|-2x+4\right|=96$$  

• $$x=-4,\ x=8$$  

• $$x=-4$$  

• $$x=-4,\ x=-8$$  

• $$x=4,\ x=8$$  

Multiple Choice

$$\frac{\left|x-5\right|}{7}=12$$  

• $$x=\left\{-84,79\right\}$$  

• $$x=\left\{-12,79\right\}$$  

• $$x=\left\{-84,84\right\}$$  

• $$x=\left\{-79,89\right\}$$  

Multiple Choice

$$-10\left|2-x\right|=-20$$  

• $$x=\left\{-4,0\right\}$$  

• $$x=\left\{0,4\right\}$$  

• $$x=\left\{-12,10\right\}$$  

• $$x=\left\{10,-12\right\}$$  

Open Ended

How did today's lesson go? How are you doing with solving Absolute Value equations?

​Review: Special Cases

​When variables cancel out of an equation, you will be left with a number equal to a number.

​

​If you get a...

• ​FALSE Statement then there is NO SOLUTION

  • ​Example: - 5 = 6

• ​TRUE Statement then it is INFINITE SOLUTIONS or All real numbers

  • ​Example: 9 = 9

Multiple Choice

Solve:

5x + 4 = 5x − 3

• x = 4

• x = -3

• infinitely many solutions

• no solutions

Multiple Choice

Solve:

2y − 3 = 2y − 3

• y = 0

• y = -3

• infinitely many solutions

• no solutions

Multiple Choice

Solve:

3(x − 2) = 3x − 6

• x = 6

• x = -6

• infinitely many solutions

• no solutions

Multiple Choice

Solve:

6(y + 4) = 6y + 10

• y = 10

• y = 24

• infinitely many solutions

• no solutions

Multiple Choice

Solve:

10x + 3 + 3x = 5x + 1 + 8x + 2

• x = -3

• x = 3

• infinitely many solutions

• no solutions

Multiple Choice

Solve:

9x + 7 − 5x = 4x − 7

• x = 7

• x = -7

• infinitely many solutions

• no solutions