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Chapter 10: Problem 65

Simplify. $$ 18-(-15)-3-(-5)+2 $$

Short Answer

Expert verified
37

Step by step solution

01

Identify the Operation Inside Parentheses

Notice that there are negative signs inside the parentheses, such as \( -(-15) \) and \( -(-5) \). We need to simplify these first.
02

Simplify the Double Negatives

Simplify \( -(-15) \) to \( +15 \) and \( -(-5) \) to \( +5 \). So the expression now becomes: \( 18 + 15 - 3 + 5 + 2 \).
03

Combine Like Terms

Add and subtract the numbers in sequence: \( 18 + 15 = 33 \), \( 33 - 3 = 30 \), \( 30 + 5 = 35 \), \( 35 + 2 = 37 \).

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Key Concepts

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

Double Negatives in Math
Double negatives can seem tricky, but they follow a simple rule. When you see two negative signs together, they become a positive. Think of it like this: negating a negative number is the same as making it positive. For example, \( -(-15) \) simplifies to \( +15 \), and \( -(-5) \) becomes \( +5 \). This rule helps us simplify expressions with double negatives more easily.

In our problem, we have \( 18-(-15)-3-(-5)+2 \). When we simplify the double negatives, we replace them with positives:

\( 18 + 15 - 3 + 5 + 2 \).
This makes it more straightforward to work with.
Basic Arithmetic Operations
Understanding basic arithmetic operations is essential to simplify expressions. The four main operations are addition, subtraction, multiplication, and division.

In our example, we focus on addition and subtraction:
  • Addition: Combining two numbers to get a sum, e.g., \( 18 + 15 = 33 \).
  • Subtraction: Finding the difference between two numbers, e.g., \( 33 - 3 = 30 \).
By performing these operations step-by-step, we can simplify complex expressions easily. Let鈥檚 sum and subtract the terms in sequence:

\( 18 + 15 = 33 \)

Now subtract 3: \( 33 - 3 = 30 \)
Add 5: \( 30 + 5 = 35 \)
Finally, add 2: \( 35 + 2 = 37 \).

Thus, the simplified expression is 37.
Combining Like Terms
Combining like terms is another important concept in algebra. It involves grouping and simplifying terms that have the same variable parts or, in this case, constants. This technique makes it easier to manage and simplify expressions.

In our exercise, all the terms are like terms (they're just numbers without variables). By combining them step-by-step, we can see how it simplifies the expression:
\( 18 + 15 - 3 + 5 + 2 \).
The rule is to add and subtract similar numbers systematically:
  • First, add 18 and 15 to get 33.
  • Then subtract 3 from 33 to get 30.
  • After that, add 5 to get 35.
  • Finally, add 2 to get 37.
Combining like terms is a fundamental skill that makes solving algebraic expressions much simpler and more organized.

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