Problem 39 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -2+[5+(-1)] $$

Step-by-Step Solution

Answer

-3.

Step 1: Evaluate the Expression Inside the Parentheses

First, solve the expression inside the parentheses: -1.

Step 2: Add the Result from Step 1 to the Outer Expression

Now, we add the result from the parentheses (4) to the number outside the parentheses: -2 + 4 = 2.

Key Concepts

Order of Operations

When solving algebraic expressions, it's essential to follow the order of operations. This ensures you consistently reach the correct answer. The order of operations can be remembered with the acronym PEMDAS:

• P: Parentheses first
• E: Exponents (like powers and square roots)
• M/D: Multiplication and Division (from left to right)
• A/S: Addition and Subtraction (from left to right)

If you follow these rules, you'll solve the expression step-by-step correctly. For example, in the given exercise \(-2 + [5 + (-1)]\), we start with the parentheses first, while other operations like addition follow later.

Parentheses in Math

Parentheses are crucial in mathematics because they indicate which operations to carry out first. Think of parentheses as a way to prioritize certain parts of an expression. For the expression \(-2 + [5 + (-1)]\), we first focus on solving inside the parentheses.
Let's break it down:

• First, we solve the inner expression: \(5 + (-1) = 4\).

This simplifies our original expression to \(-2 + 4\). Parentheses make sure we handle complex calculations in a structured sequence.

Addition with Negative Numbers

Adding negative numbers can feel tricky at first, but it's quite simple with practice. When adding a negative number, it's the same as subtracting its positive counterpart.
For instance, instead of thinking \(5 + (-1)\), you can think of it as \(5 - 1\), which equals 4.
In our original problem, once we handle the parentheses, we get \(-2 + 4 \). Now, we subtract 2 from 4, resulting in 2.

• Tip: Always look at the sign in front of the number; a negative sign tells you to subtract.

Making sense of addition involving negative numbers ensures you accurately reach solutions.