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Chapter 3: Problem 249

In the following exercises, simplify each expression. $$26-3(2-7)$$

Short Answer

Expert verified
41

Step by step solution

01

Evaluate the Parentheses

First, solve the expression inside the parentheses: \(2 - 7 = -5\)
02

Multiply by the Coefficient Outside the Parentheses

Next, multiply the result from Step 1 by the coefficient outside the parentheses: \(-3 * (-5) = 15\)
03

Perform the Addition/Subtraction

Finally, subtract the result from Step 2 from the first number in the equation: \(26 + 15 = 41\)

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Key Concepts

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

Order of Operations
When solving math problems, it's crucial to follow the order of operations. This way, everyone solves the problem the same way and gets the same answer.

Often remembered as PEMDAS, the order of operations stands for:
- **P**arentheses
- **E**xponents
- **M**ultiplication
- **D**ivision
- **A**ddition
- **S**ubtraction

This means you should first solve expressions in parentheses, then calculate exponents, follow up with multiplication or division (from left to right), and finish with addition or subtraction (from left to right). Applying PEMDAS ensures consistency and accuracy in solving equations.
Parentheses Evaluation
Parentheses tell you to solve the part of the equation inside them first. This is crucial: solve what's inside before moving on.

Let's look at the example expression: \(26-3(2-7)\).
Start by solving the expression inside the parentheses. Here, you perform:
\(2 - 7 = -5\).
By simplifying the part in the parentheses first, you accurately move forward with the right values. Ignoring this step will lead to the wrong answer, so always double-check what's inside parentheses before solving the rest.
Multiplication of Integers
After handling the parentheses, the next step is multiplication. Remember, multiplication appears before addition and subtraction in the order of operations.

Continuing from our example: \(26 - 3(-5)\).
Pretend the parentheses around -5 are invisible for a moment. Simply multiply the numbers: \(-3 \times -5 = 15\).
Notice, multiplying a negative by a negative gives a positive result. This is a key rule:
- Negative \(\times\) Negative = Positive
- Negative \(\times\) Positive = Negative
Multiplying integers correctly helps keep your calculations accurate and your final answer correct.
Addition and Subtraction
Finally, address any addition or subtraction left in the problem. Even though they are last in PEMDAS, they finalize your answer.

Let's recap using our example: After evaluating parentheses and multiplying, we have: \(26 + 15\).
Perform the addition or subtraction from left to right:
\(26 + 15 = 41\).
Be careful with signs; subtract correctly if necessary:
- For adding positive numbers, just add.
- For adding a positive and a negative, subtract and keep the sign of the larger absolute value.
Correct addition and subtraction are crucial for accurate results in math problems.

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Most popular questions from this chapter

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