Not all equations we try to solve will end with \(x\) = a specific number. Some equations may have infinitely many solutions and other equations may have no solution at all. The following video will show how to recognize these solutions.

Special Cases Equations with Infinite Solutions and Equations with No Solutions

Video Source (05:35 mins) | Transcript

There are three types of answers we can get when solving for a variable:

- \(x\) = A specific number (this is what we’ve been getting until now such as \( x = 5.3\) )
- \(x\) = All real numbers or infinitely many solutions (when we get x=x or when any number is equal to itself such as \(3 = 3\) )
- No Solutions (when we end with a false statement like \( 1 = 5 \) )

## Additional Resources

- Khan Academy: Number of Solutions to Equations (05:26 mins, Transcript)
- Khan Academy: Number of Solutions - Example (01:54 mins, Transcript)

### Practice Problems

- \(-9{\text{M}} {-} 4 = -9{\text{M}} - 4\) (Solution
- \(9 + 8{\text{T}} = 13{\text{T}} + 2\) (Solution
- \(-4 + 2{\text{b}} = 2{\text{b}} - 9\) (Solution
- \(-7 + 7{\text{b}} + 18 = 3{\text{b}} + 3 - 4{\text{b}}\) (Solution
- \(2{\text{x}} + 5 + {\text{x}} = -1 + 3{\text{x}} + 6\) (Solution
- \(2(3{\text{X}} + 4) = 6{\text{X}} + 7\) (Video Solution
- \(-4(4{\text{M}} {-} 3) = -16{\text{M}} + 12\) (Video Solution

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