Problem 29 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ (8+6)(5-3) $$

Step-by-Step Solution

Answer

28

Step 1 - Simplify Inside the Parentheses

First, simplify the expressions inside both sets of parentheses. For (8+6), we get 14. For (5-3), we get 2.

Step 2 - Multiply the Simplified Results

Next, multiply the simplified results of each set of parentheses together. Multiply 14 ∙ 2.

Step 3 - Compute the Result

Perform the multiplication. 14 ∙ 2 equals 28.

Key Concepts

Evaluating Expressions

Evaluating expressions involves finding the value of an algebraic expression by substituting numbers for variables or simply performing arithmetic operations. When you evaluate an expression, you systematically follow steps to simplify and find the result. This is crucial in algebra as it helps in solving equations and understanding the behavior of mathematical models. In our exercise, we evaluated the expression by performing basic arithmetic within parentheses and then multiplying the results.

Order of Operations

The order of operations is the sequence in which you should perform mathematical operations to ensure accurate results. The acronym PEMDAS helps remember this order:

• P: Parentheses
• E: Exponents (or powers and roots)
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

Put simply, start by solving expressions within Parentheses first, followed by Exponents. Then, move to Multiplication and Division from left to right, and finally, perform Addition and Subtraction from left to right. In our exercise, by following this order of operations, we first simplified the expressions within parentheses before moving to multiplication.

Parentheses

Parentheses play a crucial role in math by indicating which operations should be performed first. In algebra, ignoring the parentheses can lead to incorrect results because they alter the standard order of operations.
For example, in the expression \( (8+6)(5-3) \), the parentheses tell us to add 8 and 6, and subtract 3 from 5 before doing anything else. Only after these operations have been simplified inside the parentheses do we perform the multiplication.
Parentheses help in breaking down complex problems into more manageable steps, ensuring clarity and accuracy in solving algebraic expressions. Always perform the innermost parentheses first if there are multiple layers.