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That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.

Q: What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?

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You simply call it "no solution".

You just write, "No Solution."

A set would not normally have a solution. An equation or an inequality might.

In an equation, a number that stands alone is called a constant. It is a fixed value that does not change during the equation or its solution.

That's called the "solution set".

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You simply call it "no solution".

You just write, "No Solution."

You could call it "the answer" or "the solution".

The solution set is the answers that make an equation true. So I would call it the solution.

You call that a "solution" of the equation.

Single answer. Coincidental (same equation), No solution.

The Solution of an equation is the value of the variable that makes the equation truean answer

A set would not normally have a solution. An equation or an inequality might.

In an equation, a number that stands alone is called a constant. It is a fixed value that does not change during the equation or its solution.

That's called the "solution set".

The number that replaces a variable is the solution to the equation. great question, but it's only the answer.??

A linear equation in one variable. Case 1: A conditional equation: True only for a value of the variable. Ex. x + 2 = 3, True only when x is 1. Case 2: Identity Equation: Always true. Ex. x + 2 = x + 2, True for any value of x. Case 3: x + 1 = x + 5, False for any value of x. We call a solution any value of the variable that satisfies the equation, meaning if we replace the variable with that value, the equation becomes a true statement. Example: -2(x -3) = 8 - 2x -2x + 6 = 8 - 2x (add 2x and subtract 6 to both sides) 0 = 2 False. Since this equation, which is equivalent to the original equation, is false, then the original equation is also false. Meaning, there is no real number for x that could satisfy the equation. So there is no solution to the equation.