Solving Absolute Value Equations

Solving Absolute Value Equations-(Using Graphs)

Using Graphs to Solve Absolute Value Equations

Watch this video for how you can solve absolute value equations graphically.

Copy and paste the link:

https://youtu.be/jDbl-0zS59g

Absolute Value Equations (Constants or variables on both sides)

The graph of an Absolute value equation will have at least 1 "V" shaped graph, and then might have some other type of graph as well. The other graph could be a horizontal line, a diagonal line, a curve, another v, etc. Click the picture to enlarge.

Absolute Value Equations can have:

• 2 real solutions (the most)

• 1 real solution

• 0 Real Solutions

Solution Cases: (Absolute Value Equations)

• 2 REAL Solutions (An absolute value equation with two solutions will intersect the other graph twice)

• 1 REAL Solution (An absolute value equation with one solution will intersect the other graph only one time)

• NO REAL SOLUTIONS (An absolute value equation with no real solutions will not intersect)

Solving Absolute Value Equations (Everything is on one side of the equation)

Watch this video on Solving 1 Sided Absolute Value Equations or Functions

Copy and paste the link:

https://youtu.be/g-fxl0-g4xU

Multiple Choice

Determine the number of real solutions for the given absolute value equation with the given graph. (Clicking the picture will enlarge it)

• No Real Solutions

• 1 Real Solution

• 2 Real Solutions

Multiple Choice

Determine the number of real solutions for the given absolute value equation with the given graph. (Clicking the picture will enlarge it)

• No Real Solutions

• 1 Real Solution

• 2 Real Solutions

Multiple Choice

Determine the number of real solutions for the given absolute value equation with the given graph. (Clicking the picture will enlarge it)

• No Real Solutions

• 1 Real Solution

• 2 Real Solutions

Multiple Choice

How many solutions does the following equation have?

0 = -6|9x - 7|

Hint: Graph it!!! (0 = x-axis)

• no solution

• one solution

• two solutions

Solving Absolute Value Equations Graphically-(Copy and Paste the Youtube URL to see the video)

https://youtu.be/jDbl-0zS59g

Solving Absolute Value Equations (GRAPHICALLY)

• If there is a real solution, the graphs will intersect EITHER Once or AT MOST two times.

• The solution to the absolute value equation is the X-coordinate of the intersection!!

PRACTICE SOLVING

ABSOLUTE VALUE EQUATIONS

(BY GRAPHING)

Solve the next few sets of absolute value equations.

Multiple Choice

What is the reason that absolute value is always written as a positive? (Google it if you need to!!)

• Absolute value is talking about numbers so it must be positive.

• Absolute value does not always have to be positive.

• Absolute value is like a clock it has only positive numbers.

• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

|2x - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2

Multiple Choice

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

Multiple Choice

-|−2x − 1| = 11

• {-6,5}

• {5,-6}

• -6

• No Solution

Multiple Select

Solve. Select BOTH solutions.
 $5\left|7+x\right|+2=17$  

•  $-10$  

•  $3$  

•  $4$  

•  $-4$  

Multiple Choice

I -808 I

• 808
• -808

Multiple Select

Solve. Select BOTH solutions.
 $4\left|10x\right|-3=117$  

•  $\frac{57}{20}$  

•  $12$  

•  $3$  

•  $-3$  

Multiple Select

Solve. Select BOTH solutions.
 $\left|3x\right|+2=8$  

•  $\frac{10}{3}$  

•  $2$  

•  $-2$  

•  $-\frac{4}{3}$  

Multiple Choice

Absolute value is:

• The opposite of the number

• The distance away from zero

• Distance is always positive

THE END

Multiple Select

Solve. Select BOTH solutions.
 $\left|-4+x\right|=10$  

•  $6$  

•  $14$  

•  $\frac{5}{2}$  

•  $-6$  

Multiple Select

Solve. Select BOTH solutions.

 $\left|x-1\right|=3$  

• -2

• 2

• 4

• -3