no solution, infinite solution

Solving Equations Review

​Solving Equations with No Solution

​Some equations do not have one solution. Equations can also have no solution or infinitely many solutions.

​

When solving an equation that has no solution, you will obtain an equivalent equation that is not true for any value of the variable, such as 0 = 2.

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​4 - x = 8 - x

​Solve

​8h - 4 = 4(2h - 1)

​Solving Equations with Infinite Solutions

​When solving an equation that has infinitely many solutions, you will obtain an equivalent equation that is true for all values of the variable, such as − 5 = − 5.

​

​8f = 2f + 6f

Multiple Choice

How many solutions does this equation have?

8k - 4 = 8k - 4

• Infinite

• None

• One

• Two

Multiple Choice

How many solutions does this equation have?

3x = 3x - 8

• Infinite

• None

• One

• Two

Solving Complex Equations

1. Distribute

2. Combine constants and coefficients (combining like terms)

3. Move constants to one side of the equation

4. Move coefficients to the other side of the equation

5. Divide by the coefficient

Open Ended

$$3\left(5x-2\right)+10=13$$  

$$15x-6+10=13$$  

What would be the next step that you need to take? 

Open Ended

$$2\left(3x-1\right)+3=8x-4+2x$$  

Write the equation if I distribute and combine like terms. (Do not move anything to the other side)

One, None, or Infinite Solutions

One Solution - when you solve you will get x=#

No Solution - when you solve you will get a false statement, like 6=10

Infinite Solutions - when you solve you will get a true statemen, like 5=5

Multiple Choice

When you solve an equation you get 8=8. How many solutions does that equation have?

• One

• None

• Infinite

Multiple Choice

When you solve an equation you get x=4. How many solutions does that equation have?

• One

• None

• Infinite

Multiple Choice

When you solve an equation you get 5=3. How many solutions does that equation have?

• One

• None

• Infinite