Exploring the Nature of Solutions
Solve the following equations. What do you notice/wonder about the solutions?
- \(2x-3+ 1 = 2(x-1)\)
- \(5(x-1) = 3(x+2)\)
- \(4(x-2)+2 = x+3(x-2)\)
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.
