Problem 218 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 1: Problem 218

Simplify each expression. $$ 24+3(-5+9) $$

Short Answer

Expert verified

Step by step solution

Simplify inside the parentheses

Start with the expression inside the parentheses. Calculate \[ -5 + 9 = 4 \].

Multiply

Next, multiply the number outside the parentheses by the result from Step 1. Calculate \[ 3 \times 4 = 12 \].

Add

Finally, add the result from Step 2 to the remaining constant term. Calculate \[ 24 + 12 = 36 \].

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Key Concepts

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

Order of Operations

In mathematics, the order of operations is crucial to simplifying expressions correctly and consistently. The order of operations can be remembered using the acronym PEMDAS, which stands for:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Let's apply this to the given expression: 24 + 3(-5 + 9).

First, we handle the parentheses because the 'P' in PEMDAS tells us to start there.
Next, we perform the multiplication, which comes before addition according to PEMDAS.
Finally, we finish with adding the remaining numbers.

Following this sequence ensures we simplify correctly and get the right result.

Combining Like Terms

Combining like terms is an essential algebraic skill. Like terms have the same variable raised to the same power. For example, in the expression 2x + 3 + 4x - 5, both 2x and 4x are like terms because they both have the variable x. Similarly, 3 and -5 are like terms since they are constants.

Steps to combine like terms:

Identify like terms within the expression.
Add or subtract the coefficients of these like terms.

Applying this to our exercise, while the terms 24 and 3(-5 + 9) don't require combining in a traditional sense, understanding how to simplify gets you closer to the final answer. After multiplication, the terms become 'like' for straightforward addition.

Parentheses in Math

Parentheses are used in math to group parts of an expression that should be handled first. They can drastically change the outcome of a calculation. Parentheses direct you to perform the operations inside them before doing anything else.

Simplify the example expression: 24 + 3(-5 + 9).

First, calculate inside the parentheses: -5 + 9.
Then, multiply the result by the number outside the parentheses: 3 times 4.
Lastly, use the result in the remaining part of the expression.

This method ensures you respect the structure and the intended calculations within the expression.

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91影视

Simplify each expression. $$ 24+3(-5+9) $$

Short Answer

Step by step solution

Simplify inside the parentheses

Multiply

Add

Key Concepts

Order of Operations

Combining Like Terms

Parentheses in Math

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