Problem 67 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ -(8-21) $$

Step-by-Step Solution

Answer

Answer: The value of the expression $$-(8-21)$$ is $$13$$.

Step 1: Solve the expression within parentheses

First, we need to solve the expression inside the parentheses: $$ (8 - 21) $$ Subtract 21 from 8: $$ -13 $$

Step 2: Apply negation

Now, we need to apply negation to the result: $$ -(-13) $$ Negating the negative value -13 gives us: $$ 13 $$ Thus, the value of the expression $$-(8-21)$$ is $$13$$.

Key Concepts

Subtraction

Subtraction is one of the core operations in mathematics used to determine the difference between two numbers. In our exercise, we're working with the expression \(8 - 21\).

When performing subtraction:

• Identify the minuend, which is the number you start with, here, it's 8.
• The subtrahend is what is being subtracted, in this case, it's 21.
• Think of subtraction in terms of adding a negative. Instead of \(8 - 21\), you could think of it as adding the negative of 21 to 8.

In this instance, since 21 is larger than 8, subtracting 21 from 8 results in a negative number, \(-13\). This is an important concept that can affect the subsequent steps in the calculation.

Negation

Negation is simply the process of changing the sign of a number. In mathematical expressions, applying negation flips the sign from positive to negative, or vice versa.

In the given problem, after computing the subtraction \(8 - 21 = -13\), the expression \(-(-13)\) is used.

Key points about negation:

• Negating a negative number turns it into a positive number.
• The original negative number \(-13\) becomes \(13\) when negated.
• Understanding negation helps in manipulating and simplifying expressions.

This step is crucial for solving the given problem correctly, as it directly influences the final result.

Order of Operations

The order of operations is a set of rules that define the correct sequence in which to evaluate a mathematical expression. These rules ensure that everyone gets the same result when performing complex calculations.

The common acronym to remember the order is PEMDAS:

• Parentheses – first do calculations inside parentheses.
• Exponents – evaluate exponents next.
• Multiplication and Division – work these from left to right.
• Addition and Subtraction – also from left to right.

In our exercise, we first needed to calculate the expression inside the parentheses: \((8 - 21)\). This is why subtraction was tackled before negation.

Recognizing and applying the order of operations correctly is critical for achieving the right answer when multiple operations are involved.