Problem 8 - Elementary Algebra

Question

Observe the equations and state the relationship being expressed. $$ e=g-9 $$

Step-by-Step Solution

Answer

Answer: In the given equation, e is directly related to g by a difference of 9. It means that e is 9 less than g.

Step 1: Identify the variables

In this equation, there are two variables, e and g.

Step 2: Understand the equation

The given equation is: $$ e = g - 9 $$ This means that the variable e is equal to the variable g minus 9.

Step 3: State the relationship expressed

The relationship expressed is that e is directly related to g by a difference of 9. When g increases or decreases, e will be affected accordingly. We can also say that e is 9 less than g.

Key Concepts

Variables

Variables are symbols that represent unknown or changeable values in an equation or expression. In mathematical equations, they are typically denoted by letters such as \( e \) and \( g \). In the equation \( e = g - 9 \):

• \( e \) is one variable, representing an unknown value.
• \( g \) is another variable, which also represents an unknown value.

Variables allow us to create general statements in mathematical equations.
They make it possible to solve problems for multiple scenarios by assigning different numbers to the variables.

Expressions

Expressions in mathematics are combinations of numbers, variables, and operation symbols that represent a specific value or range of values.
They do not have an equality sign, differentiating them from equations. In the context of our example, \( g - 9 \) is an expression:

• \( g - 9 \) contains the variable \( g \), the number 9, and the subtraction operation.
• It describes the relationship where 9 is subtracted from \( g \).

Expressions can be simplified or evaluated by substituting values for the variables.
Here, it's used to describe how \( e \) is derived by modifying \( g \).

Mathematical Relationships

Mathematical relationships describe how variables in an equation affect each other. In our case, the equation \( e = g - 9 \) defines a direct relationship between \( e \) and \( g \).
Here's what this implies:

• \( e \) is always 9 less than \( g \). This means if \( g \) increases, \( e \) increases by the same amount, but is always 9 units less.
• If \( g \) decreases, \( e \) decreases similarly.

This relationship helps us predict the value of one variable based on the other.
Understanding these relationships is crucial, as it provides insight into how changes in one part of an equation influence others.