Problem 10 - Algebra 1: Concepts and Skills

Question

Evaluate the variable expression when \(k=3\) $$ 11+k $$

Step-by-Step Solution

Answer

The value of the expression '11+k' when \(k=3\) is \(14\).

Step 1: Substitute Given Value for Variable

Substitute the given value, \(k=3\), into the variable in the expression. This gives: \(11+3\).

Step 2: Perform Arithmetic Operation

After substitution, the problem becomes a simple addition problem. Adding the numbers gives \(14\).

Key Concepts

Substitution Method

The substitution method is a fundamental technique in mathematics, particularly useful in algebra. It involves replacing a variable in an expression with its corresponding numerical value. To grasp the concept, imagine a variable as a placeholder for a number; when given the value of that variable, you exchange the placeholder with the actual number.

For instance, with our exercise where we evaluate the expression when \(k=3\), the substitution step is pivotal. Here's how it works in simple terms: You see the variable 'k' in the expression \(11+k\), and since you're told that \(k=3\), you replace 'k' with '3', resulting in the new expression, \(11+3\). It's like solving a mystery, where 'k' is the clue and '3' is the answer you've uncovered!

Arithmetic Operations

Arithmetic operations are the building blocks of math, comprising addition, subtraction, multiplication, and division. These are the operations we use in our day-to-day number tasks. In the setting of our exercise, after applying the substitution method, we encounter an arithmetic operation — addition.

Once you've replaced the variable with its value, in this case turning \(11+k\) into \(11+3\), you can perform the arithmetic operation. Addition is the simple process of combining numbers to find their total. By adding the numbers together, 11 plus 3, you obtain the sum of 14. The ease of such operations lies in their universal application; once you understand the fundamental process, you can handle any such problems that you face in mathematics!

Algebraic Expressions

Algebraic expressions are phrases in mathematics that can include numbers, variables, and arithmetic operations. Think of them as sentences where variables like 'x', 'y', or 'k' stand in for numbers yet to be determined or assigned.

In our exercise, \(11+k\) is an algebraic expression with 'k' as the variable. Evaluating such an expression depends on knowing the value of the variable(s) and performing the indicated arithmetic operations. Understanding algebraic expressions are essential, as they represent real-world quantities and can be manipulated to solve for unknowns, form equations, and understand relationships between numbers.