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Simplifying expressions is a fundamental skill in elementary algebra. It involves transforming complex expressions into simpler ones without changing their value. This process often includes removing unnecessary parentheses, combining like terms, and following the order of operations (PEMDAS). In our exercise, we had the expression: $$5 + (-8) - (+3)$$The first step was to remove the unnecessary parentheses. In this case, the parentheses around (-8) and (+3) do not affect the values since they don’t interact with multiplication or division. So we simplify it to:$$5 - 8 - 3$$Remember to keep the negative and positive signs attached to their respective numbers even after the parentheses are removed.

Combining numbers means performing the arithmetic operations to simplify an expression. You may need to add, subtract, multiply, or divide these numbers. The goal is to reduce the expression to a single number or a simpler form. Let's walk through the combining process from our exercise.

• Our initial step: $$5 -8$$
• When you combine 5 and -8, think of it as moving 8 units left from 5 on a number line. We get -3: $$5-8 =-3$$
• Next, we combine the result with -3 by subtracting 3 from it: $$-3 - 3$$
• Subtracting another 3 from -3 continues the movement to the left on the number line, resulting in -6: $$-3 - 3 = -6$$

Addition and subtraction are fundamental arithmetic operations used to combine numbers. When dealing with positive and negative numbers, it's essential to understand the effect of these operations on different signs. Here’s a quick guide:

• Adding a positive number moves you to the right on the number line.
• Adding a negative number (or subtracting a positive) moves you to the left on the number line.
• Subtracting a negative number (or adding a positive) also moves you to the right on the number line.

In our exercise, the expression was simplified as follows:

• First, we performed: $$5 -8 = -3 $$
• Then: $$-3 - 3 = -6$$

Understanding these operations with integers helps in accurately calculating the value of algebraic expressions.