Evaluate the expression 2x+3 for x=3.
The Correct Answer and Explanation is :
To evaluate the expression (2x + 3) for (x = 3), we can substitute the value of (x) into the expression.
- Substitution: Replace (x) with (3).
[
2(3) + 3
] - Multiplication: Calculate (2 \times 3).
[
6 + 3
] - Addition: Now, add (6) and (3).
[
9
]
Therefore, the value of the expression (2x + 3) when (x = 3) is 9.
Explanation
Evaluating mathematical expressions involves substituting values for variables and then performing the necessary operations (addition, subtraction, multiplication, and division) according to the order of operations. In this case, the expression consists of a variable (x), which represents a number that can change depending on the context.
The expression (2x + 3) is linear, indicating that it will produce a straight line when graphed. The coefficient (2) in front of (x) means that whatever value (x) takes will be multiplied by (2). The (+ 3) signifies that, after the multiplication, we will add (3) to the result.
When we substitute (3) for (x), we are essentially replacing (x) in the expression with the number (3), which allows us to find a specific value based on that substitution. After performing the multiplication first (due to the order of operations), we add (3) to find the final result.
This process is fundamental in algebra, as it allows us to evaluate expressions for various values of variables. The ability to substitute and compute is critical for solving equations and understanding relationships between quantities in more complex mathematical contexts. Therefore, learning how to evaluate expressions like (2x + 3) is a foundational skill in mathematics that applies to many areas, including algebra, calculus, and beyond.