Solve the equation <(a-5)-5=3

Solve the equation (a-5)-5=3 Solving the Equation (a-5)-5=3 ...

Solve the equation (a-5)-5=3

Solving the Equation (a-5)-5=3

This equation involves a single variable, 'a', and requires a few simple steps to solve. We'll isolate 'a' by performing inverse operations to both sides of the equation.

(a - 5) - 5 = 3  a - 5 - 5 = 3  // Simplify by combining -5 and -5  a - 10 = 3  a - 10 + 10 = 3 + 10 // Add 10 to both sides to isolate 'a'  a = 13  

Understanding the Solution

The solution to the equation (a-5)-5=3 is a = 13. This means that if we substitute 13 for 'a' in the original equation, the equation will be true.

(13 - 5) - 5 = 3  8 - 5 = 3  3 = 3 // True  

Real-world Applications of Linear Equations

Linear equations like this one appear in many real-world situations. For example, they can be used in financial calculations, determining proportions in recipes, calculating distances and speeds, and in many scientific and engineering contexts.

Example: Budgeting

Imagine you have a budget of $13 for lunch. You spend $5 on a sandwich and another $5 on a drink. How much money do you have left? This can be represented by the equation (13 - 5) - 5 = remaining amount. As we've solved, the remaining amount is $3.

Frequently Asked Questions (FAQ)

How do I check if my solution is correct?

Substitute the value you found for 'a' back into the original equation. If both sides of the equation are equal, then your solution is correct.

What are inverse operations?

Inverse operations are operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division.

Why do we add 10 to both sides of the equation?

We add 10 to both sides to isolate the variable 'a'. Since 'a' is being subtracted by 10, adding 10 cancels out the subtraction, leaving 'a' by itself.

Now you can confidently solve similar linear equations!

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