Problem 116 - Prealgebra and Introductory Algebra

Question

Simplify. $$-7+9-(-3)$$

Step-by-Step Solution

Answer

The simplification of the expression \(-7+9-(-3)\) is \(5\).

Step 1: Simplify Double Negative

First, deal with the double negative. Since a minus sign in front of a negative results in a positive, rewrite the double negative as a positive. Therefore, the expression becomes \(-7+9+3\).

Step 2: Sum up the numbers

Sum all the numbers up. Use the number line or simple arithmetic to avoid mistakes. The addition leads to a result of \(5\).

Step 3: Final result

The expression \(-7+9+3\) simplifies to \(5\). Finalize this as the solution.

Key Concepts

Double Negatives

Double negatives in mathematics might seem tricky at first, but once you get the hang of them, they're quite straightforward. When you encounter a double negative in an algebraic expression, you can simplify it by turning the expression into a positive. For example, consider the expression \(-(-3)\). The two minus signs "cancel out" each other, resulting in a positive number. Thus, \(-(-3)\) becomes \(+3\).

Using double negatives correctly ensures that you are simplifying expressions accurately, and preventing any potential miscalculations. Remember, each time you see two negatives back-to-back like \( -(-x) \), you can think of it as flipping the sign to simply \(+x\).

Arithmetic Operations

Arithmetic operations are the basic math actions that we perform daily. They include addition, subtraction, multiplication, and division. This exercise focuses mainly on addition and subtraction.

When simplifying algebraic expressions, knowing which operations to perform and in what order is important. In our expression \(-7 + 9 + 3\), follow these steps:

• First, consider the order of operations: you may know it by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• In our case, there are only additions, no need for strict PEMDAS. You simply start adding from left to right.
• Add \(-7\) and \(+9\) to get \(+2\).
• Then add \(+3\) to \(+2\) to get the final result, \(+5\).

Keep these steps in mind to simplify arithmetic operations accurately every time.

Number Line

A number line is a handy visual tool that can help you solve arithmetic problems, especially when dealing with adding and subtracting numbers. Think of a number line as an infinitely stretching line with numbers placed at regular intervals.

• You can simulate moving along the number line when adding or subtracting numbers.
• For instance, start at \(-7\) on the number line. To add \(+9\), move 9 units to the right. You land on \(+2\).
• Next, to add \(+3\), move 3 more units to the right to reach \(+5\).

Using a number line helps you visualize each step of the calculation and avoid errors in sign and magnitude. It's an excellent skill to practice for simplifying complex expressions and understanding the mathematical operations involved.