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To understand inequalities involving negative numbers, it's essential to know how to multiply negative numbers correctly. When you multiply two negative numbers, the product is positive. This might seem counterintuitive at first, but here’s a simple way to grasp it:
Imagine you owe someone money (a debt). If you owe \(4 every day for 5 days, you owe a total of \)20 – think of this as \( -4 \times 5 = -20 \). Now, imagine instead of owing (negative), you are deducting your debt each day. For 5 days, you are reducing your debt each day, so you get \( -4 \times -5 = 20 \) back!
Here’s a rule to remember:

• A negative number times a negative number equals a positive number.
• A positive number times a positive number equals a positive number.
• A positive number times a negative number equals a negative number.
• A negative number times a positive number equals a negative number.

Using this, in our exercise, \( -4 \times -5 \) is simply 20, which is a positive number.

Addition is one of the basic operations you’ll often use during calculations. It’s adding two or more numbers together to get a total sum. In our exercise, after multiplying the negative numbers, we need to add 2 to the product.
We already found that \( -4 \times -5 = 20 \). Now, we add 2 to 20: \( 20 + 2 \).
Here are some tips for addition:

• Adding a positive number makes the sum larger.
• Ensure you correctly align digits when adding larger numbers.
• Use basic memory techniques, like carrying numbers over, when necessary.

The result of 20 + 2 equals 22. This part is essential to solving inequalities.

Comparison of numbers is determining whether one number is larger, smaller, or equal to another. This concept is essential in solving inequalities.
In our exercise \( -4 \times -5 + 2 \), we got the final result as 22. Now, we need to compare this with 21. Here is how you can compare:

• Look at the whole numbers. If the numbers have the same digits, compare digit by digit from left to right.
• Remember the symbols: \(\textgreater \) means 'greater than,' \(\textless \) means 'less than,' and \(\textgreater = \) means 'greater than or equal to.'

In our case, 22 is greater than 21. This makes the inequality \( 22 \geq 21 \) true.
Understanding inequalities helps to solve more complex mathematical problems.