Problem 20 - Elementary Algebra

Question

Evaluate. \(4 x+3,\) where \(x=316\)

Step-by-Step Solution

Answer

The value of the expression is 1267.

Step 1: Understand the Expression

The given expression is a linear algebraic expression: \(4x + 3\). We need to evaluate this expression when \(x = 316\).

Step 2: Substitute the Value of x

Replace the variable \(x\) in the expression with the given value. So, the expression \(4x + 3\) becomes \(4(316) + 3\).

Step 3: Calculate the Product

Calculate \(4 \times 316\). Multiply these numbers to get \(4 \times 316 = 1264\).

Step 4: Add the Constant Term

Add the constant 3 to the result from the previous calculation. So, \(1264 + 3 = 1267\).

Key Concepts

Evaluation

Evaluation is the process of finding the value of an algebraic expression by performing the operations it contains. In our example, we are tasked to evaluate the expression \(4x + 3\) when \(x = 316\). This involves calculating the final result of the expression after all steps are executed.

• First, recognize the operation structure within the expression. In this case, we have multiplication and addition.
• Evaluation helps us understand what the expression represents numerically.

By following each step and performing the necessary operations as outlined, we can determine the precise value of the expression for the specific variable input.

Substitution

Substitution is a fundamental algebraic process used to evaluate expressions or solve equations. It involves replacing a variable with a specific number. In our example, we substitute \(x\) with \(316\) in the expression \(4x + 3\). Here's how substitution works:

• Identify the variable in the expression. Here, our variable is \(x\).
• Replace each occurrence of the variable with the given numerical value. In our expression, change \(x\) to \(316\).
• This substitution transforms the expression into an arithmetic statement you can calculate: \(4(316) + 3\).

Substitution simplifies the expression, allowing us to proceed with other mathematical operations to find an answer.

Mathematical Operations

Mathematical operations are the backbone of solving algebraic expressions. They include basic arithmetic operations such as addition, subtraction, multiplication, and division. In our task, we perform two operations:**Multiplication**

• First, multiply \(4\) by \(316\). The multiplication is executed as: \(4 \times 316 = 1264\).

**Addition**

• After obtaining the product, the next operation is addition. Add the constant \(3\) to the result of the multiplication: \(1264 + 3\).

These operations together enable us to simplify and evaluate the expression efficiently. Understanding how to correctly apply these operations is crucial for accurate problem-solving in algebra.