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What an algebra equation is. I could solve linear equations, quadratic equations, and systems of equations by adding/subtracting/multiplying/dividing both sides
by MichaelDickens 4y ago
What an algebra equation is. I could solve linear equations, quadratic equations, and systems of equations by adding/subtracting/multiplying/dividing both sides of the equation and by adding two equations together. But I didn't know why you were allowed to do any of those things, or what else might be allowed. Are you allowed to square both sides? Raise both sides to a power?
It wasn't until maybe my third year of algebra that I realized an equation means both sides of the equation are equal to each other, which means you can perform any operation at all to both sides, and the result will still be equal.
- sgdpk 4y agoThis is a great example! I was fortunate enough that my father explained it to me when I was in school. An equation is like a balanced scale: whatever you do to one side, you must do to the other, to keep things balanced. I still remember that "click".
- ipnon 4y agoIt was long after I graduated and passed symbolic logic that I realized a proof is the “solution” of an equation using logical operators instead of algebraic ones. Proof writing then becomes following branches on the tree of textbook knowledge to new leaves. I envy those who grok this when they’re kids.
- kamaal 4y agoCan you elaborate more on this?
- xigoi 4y agoJust be a little careful: when solving an equation, you're usually asking when the sides are equal, not asserting that they are. So the implication has to go in the opposite order.