Solving Mathematical Expressions with Variables: A Basic Guide

Understanding how to substitute values into mathematical expressions and solve them is a fundamental skill in algebra. This guide will walk you through a practical example, demonstrating how to find the value of a given expression by substituting specific values for variables. We'll use the example of?2a - 3b where?a 3?and?b 7, to illustrate the process.

Variables in Mathematical Expressions

A variable is a symbol, usually a letter, that represents an unknown number or quantity. In the expression?2a - 3b,?a and?b are variables. Substituting specific values for these variables is a common task in algebra. We are asked to find the value of the expression when?a 3?and?b 7.

Substituting Values

The first step is to substitute the given values into the expression. The expression we are dealing with is?2a - 3b. Given that?a 3?and?b 7, we substitute these values into the expression:

2a - 3b 2(3) - 3(7)

Performing Operations

Next, we need to perform the operations as dictated by the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Multiplication

We perform the multiplication in the expression:

2(3) 63(7) 21

So, the expression now looks like this:

6 - 21

Subtraction

Finally, we perform the subtraction:

6 - 21 -15

Therefore, the value of the expression?2a - 3b when?a 3?and?b 7?is?-15.

Conclusion

Solving mathematical expressions with variables is a straightforward process once you understand the steps involved. By substituting values, performing multiplication, and then subtraction, you can find the value of the expression. This example highlights how to apply these skills in a practical scenario.

Additional Resources

For further practice and resources on this topic, consider exploring the following:

Khan Academy's Core Algebra FundamentalsMath is Fun Algebra GuideCool Math Algebra Lessons

Frequently Asked Questions

Here are some common questions and their answers related to the substitution and evaluation of mathematical expressions:

Q: What is the difference between a variable and a constant in an expression?A: A variable is a symbol that represents an unknown quantity, while a constant is a fixed number.Q: Can we use any value for the variables in an expression?A: Yes, you can use any value for the variables as long as it satisfies the context or problem given.Q: How do we handle complex expressions with multiple variables?A: The process remains the same. Substitute the values, perform multiplication and division first (from left to right), and then addition and subtraction (from left to right).

Understanding these concepts and practicing regularly will help you become more proficient in evaluating expressions with variables.