Problem 80 - Algebra 1

Question

Evaluate the expression for the given value of the variable. $$\text {y+2 when y=10}$$

Step-by-Step Solution

Answer

The result is 12.

Step 1: Identify the given values

In the exercise, the value for \(y\) is given as \(10\). The expression to be evaluated is \(y+2\)

Step 2: Substitute the given value into the expression

Replace \(y\) in the expression with \(10\): \(10 + 2\)

Step 3: Simplify the expression

Add together the numbers to simplify the expression: \(10 + 2 = 12\)

Step 4: State the result

The result of evaluating the expression \(y+2\) when \(y=10\) is \(12\).

Key Concepts

Substitution

In the realm of algebra, substitution is a fundamental technique used to evaluate expressions. This process involves replacing a variable in an algebraic expression with its numerical value. To perform substitution effectively, you first need to know what value has been assigned to the variable. In our given exercise, the variable is y, which has been assigned the numerical value of 10. With substitution, we simply replace each occurrence of y in the expression with 10, transforming the abstract expression into a concrete numerical problem we can solve.

For instance, in the expression y + 2, we apply substitution by replacing y with 10, resulting in the new expression, 10 + 2. This enables us to move on to the next stage: simplifying the expression to find our answer. Substitution is not just a method, but a stepping stone towards unlocking the solutions to more complex problems in algebra.

Simplifying Expressions

Once we've substituted the variables with their respective values, the next step is simplifying expressions. This process helps in reducing the expression to its most basic form, making it easier to understand and solve. Simplifying can involve various operations such as addition, subtraction, multiplication, division, or applying the order of operations correctly if the expression is more complex.

In the exercise provided, after substituting y with 10, we get a simple expression: 10 + 2. Now, to simplify it, we sum the numbers to get the result, which is 12. This process might seem straightforward with such a simple expression, but it forms the bedrock that students need to build upon as they tackle more advanced algebraic problems. When simplifying expressions, ensure all arithmetic is performed accurately and check the result to verify that the expression cannot be reduced further.

Algebraic Expressions

At the heart of many algebraic problems lie algebraic expressions. An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y), and operators (such as plus, minus, multiply, and divide). The power of an algebraic expression comes from its ability to represent a range of possible numbers, rather than a single value as in a numerical expression.

The core of understanding an algebraic expression is identifying the terms and how they interact with each other through the operators. In the expression y + 2, y is a variable that represents an unknown value, and 2 is a constant term. Together, they are connected by a plus operator, indicating that whatever value y takes, two will be added to it. By mastering how to work with algebraic expressions, students unlock the potential to solve a vast array of problems across different areas of mathematics.