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Chapter 9: Problem 75

Evaluate. $$ -|6|-|-11|+(-4) $$

Short Answer

Expert verified
The solution to the expression is -21.

Step by step solution

01

Evaluate the absolute values

Evaluate the absolute values of the numbers inside the absolute value symbols. For \(|6|\), the absolute value of 6 is 6, and for \(|-11|\), the absolute value of -11 is 11.
02

Apply the negations

Apply the negations to the absolute values obtained: \(-|6| = -6\) and \(-|-11| = -11\).
03

Rewrite the expression

Rewrite the original expression with the evaluated absolute values and applied negations: \(-6 - 11 + (-4)\).
04

Perform the arithmetic operations

Perform the arithmetic operations step-by-step: \(-6 - 11 = -17\), then \(-17 + (-4) = -21\).

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Key Concepts

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

Evaluate Absolute Values
To evaluate absolute values, you need to understand what absolute value means. The absolute value of a number is its distance from zero on the number line. It is always a non-negative number.
For example, the absolute value of 6 is written as \(|6| = 6\), and the absolute value of -11 is written as \(|-11| = 11\).
So, you essentially just strip away the sign and keep the magnitude of the number.

Step by step:
  • For positive numbers, \(|x| = x\).
  • For negative numbers, \(|-x| = x\).
Negation in Algebra
Negation is about changing the sign of a number. In algebra, putting a negative sign in front of a number means taking its opposite.
For instance, the opposite of \(6\) is \(-6\), and the opposite of \(-11\) is \(-(-11) = 11\).
This step often confuses students, but it becomes easier with practice.

Applying negation:
  • \(-|6| = -6\)
  • \(-|-11| = -11\)
Arithmetic Operations with Integers
Arithmetic operations with integers involve adding, subtracting, multiplying, or dividing whole numbers.
When dealing with negative integers, be especially careful with signs.
If you follow the correct order of operations, solving the problem becomes straightforward.

Let's break it down step-by-step:
  • First, we rewrite the expression with evaluated values from the previous steps: \(-6 - 11 + (-4)\).
  • Next, we perform the arithmetic operations one at a time:
  • Subtraction: \(-6 - 11 = -17\).
  • Finally, addition with another negative number: \(-17 + (-4) = -21\).
This gives us the final answer: \(-21\).

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