Problem 43 - Algebra 1

Question

Evaluate the expression for the given value of the variable. (Review 1.3 and 2.5 for 4.2 ) $$13-(y+2) \text { when } y=4$$

Step-by-Step Solution

Answer

The value of the expression \(13-(y+2)\) when y=4 is 7.

Step 1: Substitute the given value of y,

Firstly, substitute the given value of y(=4) into the equation. So, the equation \(13-(y+2)\) becomes \(13-(4+2)\).

Step 2: Simplify the bracketed expression and remainder of the equation

Then, calculate the value of the expression inside the brackets first, according to the order of operations (BIDMAS/PEDMAS). It gives us \(13 - (4+2) = 13 - 6\).

Step 3: Compute the final result

Finally, perform the subtraction to get the answer. It gives us \(13 - 6 = 7\). Therefore, the solution to the equation when y = 4 is 7.

Key Concepts

Understanding the Order of Operations

When working with mathematical expressions, it's important to perform operations in the correct order to achieve accurate results. A common guideline followed is the BIDMAS/PEDMAS rule, which stands for:

• Brackets/Parentheses
• Indices/Exponents
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

In our example, we first have to deal with the expression inside the brackets: \((y+2)\).
This requires us to perform the addition before addressing the subtraction outside the brackets. By following BIDMAS/PEDMAS, we ensure that each mathematical operation is executed in a logical sequence, minimizing errors especially in complex expressions.

Substitution in Expressions

Substitution is a simple yet powerful tool in algebra. It involves replacing a variable with a given numerical value in an expression. In this exercise, the variable \(y\) is replaced with the number 4, transforming the expression \(13-(y+2)\) into \(13-(4+2)\).
This step is crucial as it converts the abstract expression into a numeric equation that can be easily calculated. When substitution is done correctly, it simplifies the process of evaluating expressions with variables.

Simplification of Expressions

The process of simplification involves performing operations to reduce an expression to its simplest form. After substitution, the given expression becomes \(13-(4+2)\).
Utilizing the order of operations, we first simplify the operation inside the brackets to get \(4 + 2 = 6\).
Next, we perform the subtraction: \(13 - 6 = 7\). At each step, we simplify parts of the expression to eventually reach a final, simple result. Simplification is helpful for making complex or lengthy expressions more manageable and understandable.