will a one variable equation always have only one solution

Every linear equation that is a conditional equation has one solution. However, not every linear equation in one variable has a single solution. There are two other cases: no solution and the solution set of all real numbers. ... Therefore, the equation is always true.

Step-by-step explanation:

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facundo3141592 facundo3141592 · Answer 2 · 2021-11-11T11:31:27+01:00

We want to see if a one-variable equation always has only one solution.

This is false, as one-variable equations can have no solutions or more than one solution.

So we start with the statement:

"A one-variable equation always has only one solution".

We need to find a counterexample to prove that this is false, and there are really easy counterexamples, like:

x^2 - 4 = 0

This is a one-variable equation, and solving it we have:

x^2 = 4

x = ± √4 = ±2

So here we have two solutions, 2 and -2, thus the statement is false.

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