Problem 60 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \((L e s s o n \quad 1.1)\). $$ c+15 \text { when } c=12 $$

Step-by-Step Solution

Answer

The value of the expression \(c+15\) when \(c=12\) is 27.

Step 1: Identify the given values

Here, the problem gives the value of variable \(c\) which is 12.

Step 2: Substitute the variable in the expression

Substitute the value of \(c\) into the expression \(c+15\), thus replacing \(c\) with 12.

Step 3: Evaluate the expression

With the substitution, the expression becomes \(12+15\) which is equal to 27.

Key Concepts

Substitution in Algebra

Substitution in Algebra is a fundamental concept that helps in simplifying expressions and evaluating them based on given values. It essentially means replacing a variable in an expression with a specific numerical value. This process helps in finding the actual value of the expression.
For instance, consider the expression \(c + 15\). If you are given the problem to find the value of this expression when \(c = 12\), you apply substitution by replacing \(c\) with 12.

• Start with identifying the variable and its given value.
• Replace the variable in the expression with the provided number.

This simple step transforms the original expression into one involving only numbers, making it easy to evaluate using basic arithmetic operations.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These are the building blocks of mathematics and are applied in evaluating algebraic expressions once substitution is completed.
Let’s see this in action within the expression \(12 + 15\), resulted after substituting \(c = 12\) into \(c + 15\).

• For addition such as in \(12 + 15\), simply combine the two numbers to find the sum.
• If subtraction was involved, you would subtract one number from the other.
• In multiplication, you would multiply numbers together.
• For division, you divide one number by another.

The sum of \(12 + 15\) is \(27\). These straightforward operations allow us to arrive at the final result of the initial expression after substitution.

Variables in Algebra

In algebra, variables are symbols like \(c\), \(x\), or \(y\) that represent numbers. They are placeholders for values that can change or vary, hence the name “variable.” Understanding and working with variables is crucial as these are core to forming algebraic expressions.

• Variables allow for generalization of mathematical concepts, rather than focusing strictly on specific numbers.
• They are essential in creating equations that model real-world situations and help in illustrating general rules.

When given a value to substitute, like \(c = 12\), you convert the equation involving the variable into a solvable problem. This forms the basis of not only evaluating expressions but also solving more complex algebraic equations later on.