Unit 4, Lesson 10
All, Some, or No Solutions
Accelerated 7
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What do you notice? What do you wonder?
Write the other side of this equation so that this equation is true for all values of
Write the other side of this equation so that this equation is true for no values of
An equation is a statement that says that two expressions have an equal value.
The equation
It is a false statement if
The equation
Some equations are true no matter what the value of the variable is.
For example,
Equations like
Some equations have no solutions. For example,
When we solve an equation, we are looking for the values of the variable that make the equation true. When we try to solve the equation, we make valid moves assuming it has a solution. Sometimes we make valid moves and get an equation like this:
This statement is false, so it must be that the original equation had no solution at all.