Solving Algebraic Equations: A Step-By-Step Guide Using a Real-World Example

Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating those symbols. Solving algebraic equations is a critical skill that helps in understanding and solving real-world problems. In this article, we will walk through an example problem step by step, including the process of solving a linear equation. By the end, you will be able to solve similar problems with confidence.

Understanding the Problem

The problem we are going to solve is: If a number is added with three and the result is multiplied by five, then add three again and the final result is thirty.

Formulating the Equation

To solve this problem, we need to translate the given information into a mathematical equation. Let's denote the unknown number as x.

The steps in the problem can be translated as follows:

u2013 Five times the number: 5x

u2013 Adding three to the result: 5x 3

u2013 Multiplying the result by two: 2(5x 3)

u2013 The final result is 30: 2(5x 3) 30

Solving the Equation

Now, let's solve the equation step by step:

tMultiplying out the parentheses: t t

2(5x 3) 30

t

1 6 30

t tSubtracting 6 from both sides to isolate the term with x: t t

1 6 - 6 30 - 6

t

1 24

t tDividing both sides by 10 to solve for x: t t

1 / 10 24 / 10

t

x 2.4

t

Checking the Solution

To ensure our solution is correct, let's substitute x 2.4 back into the original equation:

t2(5x 3) 30
t2(5(2.4) 3) 30
t2(12 3) 30
t2(15) 30
t30 30

The equation holds true, confirming that the solution is correct.

Conclusion

Throughout this example, we successfully converted a word problem into a mathematical equation, and then used algebraic methods to solve it. By following these steps, you can solve similar problems and deepen your understanding of algebraic concepts.

Frequently Asked Questions (FAQ)

tWhat is an algebraic equation? An algebraic equation is a statement that two expressions are equal, containing one or more variables. tWhat is the importance of solving algebraic equations? Solving algebraic equations is crucial as it forms the basis for understanding and solving more complex mathematical and real-life problems. tHow can I practice solving algebraic equations? Practice is key. Solve a variety of problems, including those that involve similar algebraic equations and real-world applications.