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Chapter 1: Problem 25

Simplify. $$ (7-10)-3 $$

Short Answer

Expert verified
\(-6\)

Step by step solution

01

Perform Subtraction Inside Parentheses

Begin by simplifying the expression inside the parentheses: \( 7 - 10 \). This equals \(-3\).
02

Simplify the Expression

Now substitute \(-3\) for \(7 - 10\) in the original expression. The expression becomes \(-3 - 3\). Subtract 3 from \(-3\) to get \(-6\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Order of Operations
Understanding the order of operations is vital when simplifying algebraic expressions. This set of rules determines the sequence in which operations should be performed to ensure consistent and correct results.
  • Start with operations inside parentheses first. Always simplify what's in the parentheses before dealing with other operations outside.
  • Next, follow the PEMDAS/BODMAS rule, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
  • In the given exercise, we immediately start with the expression inside the parentheses: \( 7 - 10 \). Since there are no exponents, multiplications, or divisions, we handle the subtraction next.
By following these steps, we ensure that algebraic expressions are simplified in a consistent and logical manner. Each part is solved step by step according to a specific hierarchy.
Integer Subtraction
Integer subtraction can sometimes be challenging, especially when dealing with negative numbers. Here鈥檚 a simple way to understand it:
  • Think of the operation as moving to the left or right on a number line.
  • When subtracting a larger number from a smaller one, the result is negative. For instance, in \( 7 - 10 \), since 10 is greater than 7, the result of subtracting is \(-3\).
  • Subtracting a negative is like adding its positive counterpart. However, in this exercise, you continue with the subtraction rule.
This basic understanding helps avoid confusion with signs, especially when transitioning between positive and negative integers.
Simplification Process
The simplification process involves reducing an expression to its simplest form. This means you鈥檒l perform all operations in a clear, logical order until a single number or simplest form is achieved.
  • Begin with simplifying expressions in any parentheses. In our example, we derived \(-3\) from \(7 - 10\).
  • Continue by performing any remaining operations, such as subtraction or addition, in the expression. Here, we take \(-3\) and subtract 3, resulting in \(-6\).
  • Regularly check if additional simplification is possible or if all operations are completed. In our instance, once the expression becomes \(-6\), it is fully simplified and no further steps are needed.
Learning to systematically simplify can greatly enhance accuracy in solving algebraic expressions.

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