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Chapter 3: Problem 40

Simplify each expression. \(15-|3(8-5)|\)

Short Answer

Expert verified
6

Step by step solution

01

- Simplify inside the parentheses

First, simplify the expression inside the parentheses. Here, the expression is \(8 - 5\), which simplifies to \(3\).
02

- Multiply by 3

Next, multiply the simplified result by \(3\). So, \(3 \times 3 = 9\).
03

- Apply Absolute Value

Apply the absolute value function to the product. Since \(|9| = 9\), the result remains \(9\).
04

- Subtract from 15

Finally, subtract the absolute value from \(15\). So, \(15 - 9 = 6\).

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Key Concepts

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

prealgebra
Prealgebra is a foundational course that introduces basic mathematical concepts and operations.
It helps students build the necessary skills for higher math levels. Key aspects include:
  • Understanding and working with numbers
  • Performing operations like addition, subtraction, multiplication, and division
  • Learning about variables, expressions, and equations
Mastering prealgebra is crucial as it sets the groundwork for algebra and beyond.
absolute value
Absolute value measures how far a number is from zero on a number line. It's always a non-negative number.
Here's a closer look:
  • The absolute value of a positive number is the number itself (e.g., \(|3| = 3\)
  • The absolute value of a negative number is its positive counterpart (e.g., \(|-4| = 4\)
  • The absolute value of zero is zero (\(|0| = 0\)
Understanding absolute value is vital for simplifying expressions correctly.
order of operations
The order of operations tells us the sequence to evaluate an expression. The standard order is:
  • Parentheses (solve inside them first)
  • Exponents (powers and roots)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
This order ensures everyone gets the same result for an expression. A common mnemonic to remember it is PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
subtraction
Subtraction is taking away a number from another number. It's one of the basic arithmetic operations.
Here鈥檚 a simple way to understand it:
  • The number from which you subtract is called the minuend
  • The number you subtract is called the subtrahend
  • The result is called the difference
In our example, we subtracted 9 from 15. So, \(15鈭�9=6\). Remember, subtraction is crucial in various math problems and real-life situations.

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