Solving Algebraic Expressions: A Step-by-Step Guide

Understanding and solving algebraic expressions is a fundamental skill in mathematics. In this article, we will walk through solving a specific algebraic expression and provide a detailed explanation to make the process clear and easy to follow.

Understanding Algebraic Expressions

Algebraic expressions involve variables, constants, and arithmetic operations. An expression can be as simple as a single variable or a more complex combination of variables, constants, and operations. For instance, consider the expression 2a 5b 7c. In algebra, ab is shorthand for a multiplied by b, which we can also write as a cdot b.

Let's break down the given expression step by step:

2a 5b 7c can be written as 2 cdot a 5 cdot b - 7 cdot c.

Solving the Given Expression with Given Values

Given:

a 3, b 4, c 1

Now, let's substitute these values into the expression:

2 cdot 3 5 cdot 4 - 7 cdot 1

Step-by-step calculation:

Multiply 2 by 3: Multiply 5 by 4: Multiply 7 by 1: Combine the results:

6 20 - 7 26 - 7 19

Detailed Explanation Using Mathematical Notation

Let's use mathematical notation for a more structured understanding:

2a 5b - 7c

Substitute the values of a, b, and c:

2 cdot 3 5 cdot 4 - 7 cdot 1

Calculate each term:

6 20 - 7

Simplify the expression:

26 - 7 19

Practice Problems for Algebraic Expressions

To further enhance your understanding, let's solve a few more algebraic expressions:

Problem 1: If x 5, y 2, and z 3, find the value of 3x 2y - 4z:

Solution:

3 cdot 5 2 cdot 2 - 4 cdot 3

15 4 - 12

Problem 2: If m 7, n 3, and p 2, find the value of 4m - 5n 3p:

Solution:

4 cdot 7 - 5 cdot 3 3 cdot 2

28 - 15 6

Conclusion

By understanding and solving algebraic expressions, you can effectively manipulate and simplify mathematical problems. The key is to substitute values carefully and perform the operations in the correct order. Practice will help you master this essential skill in algebra.

Remember, the ability to simplify and solve algebraic expressions is crucial for more advanced mathematical concepts. Keep practicing, and you'll be well on your way to becoming a proficient mathematician!