What is 5x when x = 3?
a) 8
b) 15
c) 75
d) 125
The Correct Answer and Explanation is:
To find the value of (5x) when (x = 3), we will substitute the value of (x) into the expression and perform the multiplication:
[
5x = 5 \times x
]
Substituting (x = 3):
[
5x = 5 \times 3
]
Now, performing the multiplication:
[
5 \times 3 = 15
]
Thus, the value of (5x) when (x = 3) is (15).
Explanation
In mathematics, expressions can be evaluated by substituting known values into them. The expression (5x) is a linear expression where (5) is a coefficient of (x). A coefficient is a numerical factor that multiplies a variable. In this case, (5) multiplies the variable (x), which represents an unknown quantity.
When we know the value of (x), we can easily compute the result of the expression. Here, we were given that (x = 3). By substituting this value into the expression (5x), we simplify the calculation to (5 \times 3).
Multiplication is one of the fundamental arithmetic operations and involves adding a number (in this case, (3)) to itself a specified number of times (here, (5) times). Thus, (5 \times 3) can be thought of as adding (3) five times:
[
3 + 3 + 3 + 3 + 3 = 15
]
The answer is listed among the multiple-choice options as option b) 15, making it the correct choice.
Understanding how to evaluate expressions by substituting known values is a crucial skill in mathematics that forms the basis for more complex problem-solving and algebraic manipulation. It helps in developing a deeper comprehension of how variables and constants interact in mathematical expressions.