91Ó°ÊÓ

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In algebra, these symbols (often letters) represent variables that can hold different values. By using algebraic equations, we can describe relationships between different quantities and solve for unknown variables.

In our problem, the task is to find a number that, when added to 9, gives \(-26\). Here, we set up an algebraic equation: \(x + 9 = -26\), where \x\ represents the unknown number. This equation allows us to use mathematical operations to uncover the value of \x\.

By understanding and setting up such algebraic equations correctly, we can tackle a wide range of real-world problems and mathematical challenges.

Inverse operations are mathematical operations that 'undo' each other. They are crucial in solving equations because they allow us to isolate variables and find their values.

For instance, addition and subtraction are inverse operations. If we add 9 to a number and then subtract 9, we end up with the original number: \(n + 9 - 9 = n\). Similarly, multiplication and division are inverse operations.

In our exercise, we identified the equation \(x + 9 = -26\). To isolate \x\ (the variable), we perform the inverse operation of addition, which is subtraction. Subtracting 9 from both sides of the equation ( \(x + 9 - 9 = -26 - 9\) ) allows us to solve for the unknown variable, \(x = -35\). This demonstrates how inverse operations are applied to solve simple algebraic equations.

Isolation of a variable refers to manipulating an equation in such a way that we get the variable on one side of the equation by itself. This is a fundamental step in solving equations because it allows us to find the value of the unknown variable.

In our problem, the equation is \(x + 9 = -26\). To solve for \x\, we need to get \x\ by itself on one side of the equation. We do this by performing the inverse operation to both sides of the equation. Since 9 is added to \x\, we subtract 9 from both sides to undo the addition: \x + 9 - 9 = -26 - 9\. This simplifies to \x = -35\.

Once the variable is isolated, the solution to the equation becomes clear. Always remember, isolating the variable is key to solving any algebraic equation efficiently.