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Chapter 3: Problem 457

In the following exercises, simplify each expression. $$ 42-4(6-9) $$

Short Answer

Expert verified
54

Step by step solution

01

Simplify inside the parentheses

First, solve any operations inside the parentheses. For the expression \(42 - 4(6 - 9)\), subtract 9 from 6:\(6 - 9 = -3\).So the expression becomes: \(42 - 4(-3)\).
02

Multiply

Next, multiply the number outside the parentheses by the result inside. In this case, we have \(-4 \times -3\):\(-4 \times -3 = 12\).Now the expression is:\(42 + 12\).
03

Add the numbers

Finally, add the two numbers together from the simplified expression:\(42 + 12 = 54\).

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Key Concepts

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

Order of Operations
When simplifying expressions, it's crucial to follow the order of operations. This is often remembered with the acronym PEMDAS:

- **P:** Parentheses
- **E:** Exponents
- **M:** Multiplication
- **D:** Division
- **A:** Addition
- **S:** Subtraction

Always start with any operations inside parentheses, then move on to any exponents (though they aren't present here), followed by multiplication and division from left to right. Finally, handle addition and subtraction from left to right. Skipping or misinterpreting any steps will lead to incorrect results. In our example, always resolve inside the parentheses before multiplying, then perform any remaining operations.
Parentheses
Parentheses are used to group parts of an expression that should be simplified first. This is the first step in order of operations. For the expression given:
\(42 - 4(6 - 9)\),
you must simplify the operation inside the parentheses first. Inside the parentheses, we have: \(6 - 9 = -3\).
So, the expression becomes: \(42 - 4(-3)\).

Parentheses impact the order in which you do operations, making sure expressions are simplified correctly and logically.
Multiplication
After resolving parentheses, the next operation is often multiplication. Using our expression \(42 - 4(-3)\),
we multiply the number outside the parentheses by the result inside. Here, it鈥檚 \(-4 \times -3\).
Multiplying two negative numbers results in a positive number, so \(-4 \times -3 = 12\).

Now your expression is \(42 + 12\). The final step is straightforward addition: \(42 + 12 = 54\). Providing easy steps ensures that students understand the necessary methods to simplify expressions correctly.

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Most popular questions from this chapter

In the following exercises, determine whether each number is a solution of the given equation. $$ 8 u+24=-32 $$ $$ \begin{array}{l}{\text { (a) } u=-7} \\ {\text { (b) } u=-1 \quad \text { (c) } u=7}\end{array} $$

In the following exercises, simplify each expression. $$ -33+(-67) $$

In the following exercises, evaluate. $$ 3 m-2 n \text { when } m=6, n=-8 $$

In the following exercises, translate and solve. Eight less than \(y\) is \(-32\)

In the following exercises, simplify. $$ -7-(-3) $$
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