Solving for the Subtracted Number: An Algebraic Approach

Algebra is often seen as an abstract and challenging branch of mathematics, but its principles are incredibly useful in real-life problem-solving. In this article, we will explore how to solve the problem of finding the number that should be subtracted from -45 to get -3. This process involves setting up an equation and using algebraic techniques to isolate the variable we are solving for. Understanding these methods will not only help you solve this specific problem but also equip you with tools to tackle various algebraic challenges.

Setting Up the Equation

Let's begin by setting up the equation. We need to find a number, x, that when subtracted from -45, gives us -3. This can be represented as:

[-45 - x -3]

To solve for x, our goal is to isolate x on one side of the equation. Let's go through the steps in detail.

Step 1: Add 3 to Both Sides

Our first step is to get rid of the -3 on the right side of the equation. We can do this by adding 3 to both sides of the equation. This action maintains the equality while simplifying the right side.

[-45 - x 3 -3 3]

By simplifying the right side, we get:

[-45 - x 3 0]

Let's combine like terms on the left side:

[-42 - x 0]

Step 2: Add 42 to Both Sides

Our next step is to isolate x. We can do this by adding 42 to both sides of the equation, which cancels out the -42 on the left side:

[-42 - x 42 0 42]

By simplifying both sides, we get:

[- x 42]

Step 3: Solve for x

The final step is to solve for x. Since x is being multiplied by -1 (indicated by the minus sign in front of x), we can eliminate this by multiplying both sides of the equation by -1:

[-1 cdot -x -1 cdot 42]

Which simplifies to:

[x -42]

Therefore, subtracting -42 from -45 (-45 - (-42)) will result in -3.

Real-World Application

Understanding how to solve such equations has real-world applications. For example, in finance, negative numbers might represent debt or expenses. If you were tracking expenses and needed to identify a specific expense amount that was recorded incorrectly, setting up an equation like this could help in identifying the exact item that was incorrectly entered.

Similarly, in physics, understanding the relationships between variables can help in solving more complex problems. If you were calculating the velocity or distance of an object moving in a particular direction, setting up equations using this method could help in finding the variables involved.

Conclusion

Algebraic equations, such as the one we solved in this tutorial, are versatile and have numerous practical applications. By mastering these techniques, you can solve a wide range of problems, from simple arithmetic to more complex real-world scenarios. Understanding how to isolate variables, adding and subtracting terms, and multiplying by coefficients can greatly enhance your problem-solving skills in both academic and practical contexts.

Keep practicing, and you'll find that solving algebraic equations becomes second nature, making your journey through mathematics smoother and more enjoyable!