In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division. Evaluating an algebraic expression means finding its numerical value when the variables are replaced with specific numbers. This process is fundamental to solving equations and understanding how variables interact within mathematical relationships.
The Problem: 2(x-9) when x=10
We are given the expression 2(x-9) and asked to find its value when x is equal to 10. To do this, we will follow a systematic approach:
Substitution: Replace the variable ‘x’ in the expression with its given value, 10. This gives us:
2(10 – 9)
Simplify inside the Parentheses: Perform the operation inside the parentheses first, following the order of operations (PEMDAS/BODMAS):
2(1)
Multiplication: Finally, multiply 2 by 1:
2
Therefore, the result of 2(x-9) when x=10 is 2.
Understanding the Process
Evaluating algebraic expressions involves several key concepts:
- Variables: These are symbols (usually letters) that represent unknown values. In our example, ‘x’ is the variable.
- Constants: These are fixed numerical values that do not change. In our example, 2 and 9 are constants.
- Order of Operations: This set of rules dictates the sequence in which operations should be performed to ensure consistent results. The acronym PEMDAS/BODMAS helps remember the order:
- Parentheses/ Brackets
- Exponents/ Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Real-World Applications
Evaluating algebraic expressions is a crucial skill with numerous real-world applications:
- Calculating Costs: Imagine you’re buying ‘x’ number of items that cost $5 each. The total cost can be represented by the expression 5x. If you buy 10 items (x=10), evaluating the expression gives you the total cost: 5(10) = $50.
- Calculating Area: The area of a rectangle is found using the formula A = l*w, where ‘l’ is the length and ‘w’ is the width. If you know the length is 12 units and the width is 5 units, you can evaluate the expression to find the area: 12 * 5 = 60 square units.
- Predicting Outcomes: In science and engineering, algebraic expressions are used to model and predict various phenomena. For example, the distance traveled by an object can be expressed as d = vt, where ‘d’ is distance, ‘v’ is velocity, and ‘t’ is time. By evaluating this expression with known values for velocity and time, you can predict the distance traveled.
Conclusion
Evaluating algebraic expressions is a fundamental skill in mathematics that allows us to understand and apply mathematical relationships in real-world scenarios. By following the steps of substitution, simplification, and adhering to the order of operations, we can confidently find the numerical value of any algebraic expression.