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Chapter 1: Problem 93

Evaluate the given expression. Remember to follow the order of operations. $$9-4[6-2(3-1)]$$

Short Answer

Expert verified
The value of the expression is 1.

Step by step solution

01

- Evaluate innermost parentheses

Start by evaluating the expression inside the innermost parentheses. In this case, it's \(3-1\). So, \(3-1 = 2\).
02

- Substitute and simplify

Next, substitute the computed value back into the expression. The expression becomes \(9-4[6-2(2)]\). Then simplify inside the brackets: \(2 \times 2 = 4\). So it becomes \(9-4[6-4]\).
03

- Evaluate inside brackets

Now, evaluate the expression inside the brackets: \(6-4 = 2\). The expression is now \(9-4[2]\).
04

- Final multiplication and subtraction

Multiply the number inside the brackets by 4: \(4 \times 2 = 8\). Finally, subtract from 9: \(9-8 = 1\).

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Key Concepts

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

Parentheses Evaluation
Parentheses tell us which operations to perform first. It's like having a secret code that tells you where to start. In our example, the innermost parentheses are \(3-1\). First, we solve \(3-1=2\). Always look for the deepest nested parentheses first, and solve them step by step. This method ensures we handle complex expressions correctly. Parentheses can sometimes be nested within other parentheses or brackets, so always work from the inside out.
Substitution and Simplification
Substitution and simplification help us manage complex expressions by breaking them into manageable parts. After solving the innermost parentheses \(3-1=2\), replace it in the original expression: \(9-4[6-2(2)]\). Simplify what鈥檚 inside the brackets next: \(2 \times 2 = 4\). The expression now looks simpler: \(9-4[6-4]\). Each simplification step makes the problem easier to solve. Remember to always replace the solved part back into the expression to maintain accuracy.
Bracket Simplification
Brackets work similarly to parentheses but usually appear in larger or more complex expressions. After substitution, the expression becomes \(9-4[6-4]\). Simplify inside the brackets: \(6-4=2\). Now, the expression is reduced to \(9-4[2]\). Just like with parentheses, always simplify the operations inside the brackets first. This approach helps you maintain the proper order of operations and keeps your work neat and organized.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. These operations follow a specific order, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). After solving inside the brackets, the expression is \(9-4[2]\). Multiply next: \(4 \times 2 = 8\). Finally, subtract: \(9-8=1\). This order ensures everyone solves the expression the same way, avoiding confusion and errors. Stick to the order of operations to get correct results every time.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$\frac{10+2(5+3)}{2 \cdot 5+3}$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$\frac{-15}{2}$$

Evaluate the given expression. Remember to follow the order of operations. $$5+\\{2+4[3+3(4+2)]\\}$$

Explain how you could use the commutative and/or associative properties to make the following computations easier to do. (a) \(-1.7+12.9-8.3\) (b) 10( 7)\((-2.3)\) (c) \(\frac{-10(3.2)}{-1.6}\) (d) \(-30\left(\frac{1.6}{3}\right)(-10)\)

Sketch the given set on a number line. $$\\{x |-3 \leq x \leq 2\\}$$
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