Evaluate the expression 4x+x for x=10.

Evaluate the expression 4x+x for x=10.

A. 30

B. 40

C. 50

D. 60

The Correct Answer and Explanation is:

To solve the expression (4x + x) for (x = 10), we start by substituting the value of (x) into the expression:

1. Substitute: Replace (x) with 10 in the expression:
   [
   4(10) + 10
   ]
2. Multiply: Calculate (4 \times 10):
   [
   4 \times 10 = 40
   ]
   Now the expression becomes:
   [
   40 + 10
   ]
3. Add: Add the two numbers:
   [
   40 + 10 = 50
   ]

So, the value of the expression when (x = 10) is 50. Therefore, the correct answer is:
C. 50

Explanation:

When evaluating algebraic expressions, you start by substituting any known values for the variables, which in this case is (x = 10). The expression (4x + x) includes both multiplication and addition. Let’s break down each step:

1. Understanding the Terms: In the expression (4x + x), the term (4x) represents (4) times (x), and the term (x) represents a single instance of (x). When combined, the expression (4x + x) can also be thought of as combining like terms: (4x + x = 5x).
2. Combining Like Terms: Simplifying (4x + x) to (5x) makes it easier to evaluate. For any given value of (x), you simply multiply by 5 rather than dealing with each term separately. Substituting (x = 10) into (5x) yields:
   [
   5 \times 10 = 50
   ]
3. Importance of Order of Operations: Following the order of operations (multiplication before addition) ensures accurate results. Here, the multiplication step ((4 \times 10)) is completed first, followed by the addition.

Why This Matters

In algebra, expressions like (4x + x) are common, and knowing how to simplify by combining like terms can speed up calculations. Understanding the process is important, especially as problems become more complex and involve multiple steps. Practicing with expressions like this builds a foundation for solving larger algebraic equations.