91Ó°ÊÓ

Negative numbers are numbers less than zero. They are commonly used to represent situations like debts, temperatures below zero, or any instance where you have 'less than nothing'. In mathematics, negative numbers are written with a minus sign (-) in front of them. For example, -3 is a negative number.

When dealing with negative numbers in inequalities, it's important to remember that they are always lower in value than positive numbers or zero.

• -5 is less than -2
• -1 is less than 0
• -10 is definitely less than 5

Additionally, multiplying or dividing inequalities by negative numbers will flip the inequality sign. For example, if we have -a > 3, dividing by -1 will flip the sign and give us a < -3.

Understanding how to work with negative numbers is key in formulating and solving inequalities in algebra.

In algebra, variables are symbols used to represent numbers. They are often letters like a, b, x, and y.

Variables are very useful for expressing general statements and equations because they can take on multiple values. When you see a statement saying 'a is negative', the letter 'a' is the variable, and it represents an unknown number that we know is less than zero.

• If 'a' is our variable, any value it could represent, like -1, -2.5, or -100, would all be valid since they are negative numbers.

When you use variables in inequalities, they help in setting up equations to find the range of possible values. For example, 'a < 0' tells you that the variable 'a' must be some number less than zero.

Formulating inequalities is a way to express that one quantity is either smaller or greater than another. Inequalities use symbols like <, >, ≤, and ≥.

In the exercise, when the statement says 'a is negative', you need to represent this condition using an inequality. Saying that 'a is negative' means that 'a' must be less than zero. Therefore, you write the inequality as:

\( a < 0 \)
This clearly states that 'a' is any number less than zero.

• The < symbol means 'less than'.
• By writing 'a < 0', you are formulating an inequality that precisely captures the statement.

Inequalities are an essential part of algebra because they help to define ranges and give conditions under which certain statements are true. Make sure to always think about what the inequality is stating and check your solutions to confirm they make sense within that statement.