LINR 2 | Lesson 1 | Explore (Nature of Solutions)

Exploring the Nature of Solutions

Solve the following equations.  What do you notice/wonder about the solutions?

  1. \(2x-3+ 1 = 2(x-1)\)
  2. \(5(x-1) = 3(x+2)\)
  3. \(4(x-2)+2 = x+3(x-2)\)

Solutions:  One solution, no solution, and infinitely many solutions respectively.


Notes: A linear equation can have one solution, no solution, or an infinite number of solutions.

  • An equation of the form \(x+a = x+a\) has infinite solutions since you can use any value for \(x\) and this statement will always be true.
  • An equation of the form \(x+a = x-a\) has no solutions since there is no value for \(x\) that will make this statement true.
  • An equation of the form \(x+a = b\) has one solution since there is only one value for \(x\) that will make this statement true.

Go to Try This! (Solving Equations)