Special Solutions Equations

Solving equations with special solutions

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No Solution (NS)

• Note that we have variables on both sides of the equation. So we will subtract 3x from both sides to eliminate the 3x on the right side of the equation. However, something odd happens

• That can't be right! We know that 5 does not equal 2.

• It is a false statement to say that 5=2, so we know that there can be no solution.

Infinite solution (IS)

• We have variables on both sides of the equation. So we will subtract 3x from both sides to eliminate 3x on the right side of the equation. However, something odd happens.

• When does 2 = 2? All the time! This means  that i does not matter what value we substitute for x, the equation will always be true.

• Sometimes we use the infinity symbol♾️ to represent infinite solutions.

One Solution

• Let's not forget what we already know!

• We have looked at equations where there is exactly 1 solution

Multiple Choice

What is the solution to this equation?

$$2x+5=2x-3$$  

• x=2

• Infinite Solutions (IS)

• No Solution

Multiple Choice

Solve:

$$2x+1=2x-1$$  

• No Soltuion (NS)

• Infinite Soltion (All Real Numbers)

• x=0

Multiple Choice

3x+15=3(x+5)

• No Solution (NS)

• Infinite Solution( All Real #'s, IS)

• x=15

Multiple Choice

$$3x-8=3\left(x-4\right)+1$$  

• $$x\ =\frac{19}{6}$$  

• Infinite soltuions (all real #'s, IS)

• No Soltuion (NS)

Poll

How do you feel about today's lesson?

• I could teach this to a student who was absent.

• With some practice I know I will get better.

• I might need you to look at my answers when I'm working independently but I know I can do it.

• I have no idea where the numbers were coming from.