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.

Try This!

Go to Try This! (Solving Equations)