Understanding Solutions in Mathematics | A Comprehensive Explanation and Examples

What is a solution

In mathematics, a solution refers to the value or values that satisfy a given equation, inequality, or system of equations

In mathematics, a solution refers to the value or values that satisfy a given equation, inequality, or system of equations. It is the answer or the set of values that make the equation or inequality true.

For example, consider the equation 2x + 3 = 9. To find the solution, we need to determine the value of x that satisfies this equation. We can solve this equation by isolating the variable x:

2x + 3 = 9
Subtracting 3 from both sides:
2x = 6
Dividing both sides by 2:
x = 3

So, in this case, the solution to the equation 2x + 3 = 9 is x = 3. When we substitute x = 3 back into the equation, we can see that 2(3) + 3 equals 9, making the equation true.

In some cases, an equation may have multiple solutions. For example, the equation x^2 = 9 has two solutions: x = 3 and x = -3, as both values satisfy the equation when substituted. These solutions are sometimes referred to as the “roots” of the equation.

It’s important to note that not all equations have solutions. In such cases, the equation is said to be “inconsistent” or “unsolvable.” For example, the equation x^2 = -9 has no real solutions because no real number squared can result in a negative value. However, if we consider complex numbers, the equation does have two complex solutions: x = 3i and x = -3i.

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