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Chapter 1: Problem 25

Evaluate each of the following expressions, if possible. $$5-(3-7)$$

Short Answer

Expert verified
9

Step by step solution

01

Simplify the inner parentheses

First, determine the value inside the parentheses. Evaluate the expression inside the inner parentheses: \[3 - 7 = -4\]
02

Substitute the simplified value

Next, substitute the value obtained from Step 1 back into the original expression: \[5 - (-4)\]
03

Simplify the outer expression

Now, simplify the outer expression. Subtracting a negative number is equivalent to adding the absolute value of that number. So: \[5 - (-4) = 5 + 4 = 9\]

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Key Concepts

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

Inner Parentheses
When solving expressions with multiple parentheses or brackets, it's crucial to start with the innermost ones.
This concept helps us break down a complex problem into smaller, manageable parts.

In the given exercise, the innermost parentheses contain the expression \(3 - 7\).
We handle this part first to simplify the expression step-by-step.

Steps to solve inner parentheses:
  • Identify the innermost parentheses
  • Evaluate the expression inside it
  • Replace the parentheses with its value in the original expression

Let's illustrate it using the exercise: \(5 - (3 - 7)\)
The innermost part is \(3 - 7\).
Calculating this, \(3 - 7 = -4\).

Now, we substitute -4 back in place of \(3 - 7\).
So, the expression becomes \(5 - (-4)\).
Substitution
Once you've simplified the inner parentheses, the next step is substitution.
Substitution means replacing the simplified value back into the original expression.

Let's see this process using our example exercise:

After simplifying the inner parentheses \(3 - 7\) to \(-4\), we substitute \(-4\) in the original expression:

\

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$30 \div(5 \cdot 2)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$5.2-1.4(2.8-0.7)$$

Evaluate the given expression. Remember to follow the order of operations. $$6+(4 \cdot 3)+2$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$2 \frac{1}{3}$$

In Exercises \(73-84\), evaluate the given expression. $$7-3(5-1)$$
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