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Chapter 1: Problem 70

Evaluate the given expression. Remember to follow the order of operations. $$30-5(4-2)$$

Short Answer

Expert verified
The expression evaluates to 20.

Step by step solution

01

Evaluate Inside Parentheses

First, solve the expression inside the parentheses. Evaluate \(4 - 2\).
02

Multiply

Next, multiply the result from inside the parentheses by 5. Calculate \(5 \times 2\).
03

Subtraction

Finally, subtract the result of the multiplication from 30. Evaluate \(30 - 10\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Evaluating Expressions
Evaluating expressions means finding the value of an algebraic expression by following a set of rules. This process is crucial in algebra, as it helps solve and simplify problems. Let鈥檚 go through the steps using our given expression:
1. **Identify the Operations**: In our example, we have subtraction and multiplication.
2. **Follow the Order of Operations**: Apply operations in the correct sequence. Commonly remembered by the acronym PEMDAS:
  • **P**arentheses
  • **E**xponents
  • **M**ultiplication and **D**ivision (left to right)
  • **A**ddition and **S**ubtraction (left to right)
Using PEMDAS ensures that you evaluate every expression correctly. In the given expression, 30-5(4-2), you would start by solving inside the parentheses, then multiplication, and lastly subtraction.
Parentheses in Algebra
Parentheses group parts of an expression that should be evaluated first. This helps to clarify which operations should happen before others. For the expression provided,
**Step 1: Solve Inside Parentheses**Starting with the expression: 30-5(4-2), we first evaluate inside the parentheses: \( 4 - 2 \) results in 2.
Parentheses help you organize the order of operations and prevent mistakes in more complex expressions. By always starting with the innermost parentheses, you ensure that you鈥檙e following the right steps. For instance, if parentheses were nested like this: (3+(2-1)), you'd first solve the innermost expression \(2-1\) before moving to the outer ones.
Multiplication and Subtraction
After evaluating parentheses, multiplication and subtraction follow in the order of operations.
**Step 2: Multiplication**In our example: 30-5(4-2), after solving inside the parentheses, you get 30-5(2).
Next, multiply 5 and 2: \( 5 \times 2 \) which equals 10.
**Step 3: Subtraction**Finally, perform the subtraction: \( 30 - 10 \)=20.
By following these steps carefully, you can accurately evaluate any algebraic expression. Multiplication is prioritized over subtraction, so always calculate multiplication results before subtracting in order to avoid errors. Remember this order for more reliable calculations.

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Most popular questions from this chapter

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