Solving Equations with Given Values: A Step-by-Step Guide

Understanding and solving algebraic equations with given values is a fundamental skill in mathematics. In this article, we will walk you through the process step-by-step, using the equation (4x - 2y 52) with the given value (y 4).

Substitution and Simplification

When solving an algebraic equation with specific values given for certain variables, the first step is substitution. This means replacing the given values in the equation where they appear. For our equation, (4x - 2y 52), and with (y 4), we proceed as follows:

Substitute (y 4) into the equation: (4x - 2(4) 52) Simplify the equation by performing the multiplication: (4x - 8 52) Next, isolate the term with the variable (x) by adding 8 to both sides of the equation: (4x - 8 8 52 8) (4x 52 8) Simplify the right-hand side: (4x 60) Finally, solve for (x) by dividing both sides of the equation by 4: (x frac{60}{4}) (x 15)

Verification and Conclusion

By following these steps, we have determined that the value of (x) is 15. To verify the solution, you can substitute (x 15) and (y 4) back into the original equation (4x - 2y 52): Substitute (x 15) and (y 4) into the equation: (4(15) - 2(4) 60 - 8 52)

Since the equation holds true, our solution is correct.

Additional Tips for Solving Algebraic Equations

Always check your work: Double-check calculations and ensure that the final solution satisfies the original equation. Use a consistent method: Practice the same method each time to avoid errors and build confidence. Understand the variables: Clearly identify what each variable represents in the context of the problem. Precision is key: Ensure you use the correct math symbols and notation.

Frequently Asked Questions (FAQ)

Here are some frequently asked questions related to solving equations with given values:

Q: How do I solve for a variable in an equation?

A: To solve for a variable, isolate the variable on one side of the equation. Typically, you do this by performing the same operation on both sides of the equation to maintain equality. Use substitution if you have specific values to substitute for given variables.

Q: Can I use an online calculator for solving equations?

A: Yes, there are numerous online calculators available that can help you solve algebraic equations. These tools can be particularly useful for checking your work or for more complex equations.

Q: What if I don't have specific values for the variables?

A: If you do not have specific values, you can still solve for one variable in terms of the others. This is known as solving the equation for a variable. For instance, in the equation (4x - 2y 52), you can solve for (x) in terms of (y).

By following these steps and tips, you will become more adept at solving algebraic equations with given values. Practice regularly to build your skills, and don't hesitate to use online resources and tools to assist you.