Unit 4, Lesson 7
Inequivalent Equations?
Algebra 2
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Tyler was solving this equation:
He said, “I can add 1 to each side of the equation and it doesn’t change the equation. I get .”
Figure A
Figure B
Priya said, “But the graphs show that there are two solutions!” What went wrong?
Every positive number has two square roots. You can see this by looking at the graph of :
When we have a square root in an equation like , we can isolate the square root and then square each side:
But sometimes, squaring each side of an equation gives results that aren’t solutions to the original equation. For example:
Note that 36 is not a solution to the original equation, because doesn’t equal 0. In fact, has no solutions, because it’s impossible for the sum of two positive numbers to be zero.
Remember: Sometimes the new equation has solutions that the old equation doesn’t have. Always check your solutions in the original equation!