Problem 30 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ (9+5)(6-2) $$

Step-by-Step Solution

Answer

56

Step 1: Evaluate the expression inside the first parenthesis

First, solve the expression inside the first parenthesis: \(9 + 5\).Calculate: \[9 + 5 = 14\]

Step 2: Evaluate the expression inside the second parenthesis

Next, solve the expression inside the second parenthesis: \(6 - 2\).Calculate: \[6 - 2 = 4\]

Step 3: Multiply the results

Now, multiply the results from Step 1 and Step 2: \(14 \times 4\).Calculate: \[14 \times 4 = 56\]

Key Concepts

Evaluating Expressions

Evaluating expressions means calculating the value of an expression by following the rules of mathematics. In our case, we want to find the value of \( (9+5)(6-2) \). To do this confidently:

• Identify and focus on each part of the expression.
• Apply the order of operations correctly.

Evaluating expressions often involves several steps to simplify the problem, such as performing operations within parentheses first. Making sure each step is followed carefully will lead you to the correct answer.

Parentheses

Parentheses indicate which part of an expression should be calculated first. Here, we have two sets of parentheses: \( (9+5) \) and \( (6-2) \). Always evaluate expressions inside parentheses before performing other operations.
1. Start with \( (9+5) \). Solve inside first: \( 9 + 5 = 14. \)
2. Next, solve \( (6-2) \). Calculate: \( 6 - 2 = 4. \)
Now you have simplified the expression inside each parenthesis to find: \( 14 \) and \( 4. \)
This simplifies further calculations and ensures accuracy in our solution.

Multiplication

Once the expressions within the parentheses are evaluated, the next step is to perform multiplication. This means taking the results from each set of parentheses and multiplying them together.
1. You have \( 14 \) from \( (9 + 5) \) and \( 4 \) from \( (6 - 2). \)
2. Multiply these results together: \( 14 \times 4 = 56. \)
Multiplication combines these two numbers to give you the final value of the evaluated expression, ensuring that all parts of the expression are correctly accounted for.
Understanding each step ensures that complex problems can be broken down into manageable parts, leading you to the correct solution.