Problem 24 - Elementary and Intermediate Algebra

Question

Find \(-x\) when \(x\) is each of the following. $$ 13 $$

Step-by-Step Solution

Answer

-13

Step 1: Identify the Value of x

Understand that the given value of x is 13.

Step 2: Apply the Negative Sign

To find \(-x\) when \(x = 13\), you need to apply the negative sign to the given value. Therefore: \(-x = -13\).

Key Concepts

negative sign

The negative sign is a symbol used in mathematics to denote that a number is less than zero. It is represented by a hyphen (-) before the digit.

When we see a negative sign in front of a number, it means we are dealing with a negative number. For instance, -13 denotes negative thirteen.

The presence of a negative sign also indicates the direction on a number line. Positive numbers are located to the right of zero, while negative numbers are to the left.

In the exercise at hand, we are asked to find the value of -x given x = 13. By placing a negative sign before 13, we end up with -13. This simply means that -13 is 13 units to the left of zero on the number line.

integer operations

Integer operations involve basic arithmetic with whole numbers (both positive and negative).

The primary operations include addition, subtraction, multiplication, and division. Working with negative integers in these operations follows specific rules.

For the given exercise, we focus on the concept of negation, which is the arithmetic operation of changing a number's sign.

When you negate a positive number, it becomes negative, and vice versa. This means applying a negative sign before a positive integer (like 13) will result in a negative integer (like -13). These rules ensure consistency in mathematical calculations.

Additionally, when performing other integer operations with negative numbers, remember:

• Adding a negative number is the same as subtraction.
• Subtracting a negative number is the same as addition.
• Multiplying or dividing two negative numbers results in a positive number.
• Multiplying or dividing a negative number by a positive number results in a negative number.

algebraic manipulation

Algebraic manipulation refers to the various techniques and processes used to simplify and solve algebraic expressions and equations.

One of the fundamental skills in algebra is handling negative numbers and applying the correct operations.

In this exercise, we are given an expression -x where x is 13.

As part of algebraic manipulation, we substitute x with its value and apply the negative sign to simplify the expression. This gives us

• -x when x = 13 becomes -13.

Mastering these basic manipulations is crucial for tackling more complex algebraic problems and equations in the future.

It's important to follow systematic steps for clarity and accuracy when dealing with algebraic manipulations.

Consistently practice to gain proficiency!