Problem 63 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \((L e s s o n \quad 1.1)\). $$ 25-y \text { when } y=14 $$

Step-by-Step Solution

Answer

The evaluation of the expression '25 - y' when y = 14 gives 11.

Step 1: Identify the given variable

In the given problem, the value of the variable y=14 is given.

Step 2: Substitute the value of variable

Now, substitute the value of y in the expression '25 - y'. It gives '25 - 14'.

Step 3: Simplify the expression

After substituting the value of y in the expression, simplify it to get the answer. The expression '25 - 14' evaluates to 11.

Key Concepts

Substitution in Algebra

In algebra, substitution is an essential technique used when a variable in an expression is replaced with its corresponding numerical value. It's much like following a recipe where you replace the ingredients with things you have in your kitchen. Consider the expression 25 - y. Here, think of y as a placeholder for a number that we don’t yet know.

When the problem states that y=14, our job is to replace y with 14. This process is what we refer to as 'substituting' the value in. So in practice, the expression becomes 25 - 14 after we replace y with its given value. Substitution is the first step towards evaluating an algebraic expression and is a fundamental concept that students must understand to progress in algebra.

Simplifying Algebraic Expressions

Once substitution has been completed, the next step in solving algebraic expressions is simplification. Simplifying an expression means reducing it to its most basic form, making it as easy as possible to understand and solve. It involves performing all the operations like addition, subtraction, multiplication, and division.

In our example where we substituted 14 for y, simplifying the expression means carrying out the subtraction: 25 - 14, which equals 11. This simplified result tells us the value of the original expression when y is 14. Simplification is about making an algebra problem easier to handle, resulting in a straightforward number rather than a more complex expression.

Algebraic Expressions and Variables

An algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols. Variables, represented by letters such as x, y, and z, are symbols that stand in for unknown values and can change or vary. These variables are the ingredients that give algebra its flexibility and power.

In the example 25 - y, y is the variable. It's important to understand that the value of an algebraic expression can change depending on the values ascribed to its variables. In our case, when y equals 14, we have one numerical value. If y were to take on a different value, our final answer in simplifying the expression would change as well.