/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Simplify the given expression. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 48

Simplify the given expression. $$ 9-8[6-(2+3)] $$

Short Answer

Expert verified
The simplified expression is 1.

Step by step solution

01

Simplify Inside the Parentheses

Begin by simplifying the expression inside the parentheses. Here we have \(2 + 3\).\[2 + 3 = 5\]
02

Replace and Simplify Inside the Brackets

Substitute the simplified value back into the expression inside the brackets and solve.\[6 - 5 = 1\]
03

Multiply by the Factor in Front of the Brackets

Multiply the simplified value inside the brackets by the number in front of the brackets, which is \(-8\).\[-8 \times 1 = -8\]
04

Final Calculation

Subtract the result from the multiplication from 9.\[9 - 8 = 1\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Parentheses
In math, parentheses are symbols used to group parts of an expression. They tell us which operations to perform first. This is part of the "order of operations," a set of rules that helps everyone get the same answer when solving math problems.

When you see parentheses like \((2 + 3)\), it means you should solve what's inside them first. So, \(2 + 3 = 5\). After simplifying what's inside, you can replace the expression with the result, which helps to make the next steps easier.

Always remember:
  • Operations inside parentheses are completed first.
  • Parentheses override other operations, like addition and subtraction outside them.
They play a crucial role in getting the correct result of an expression.
The Role of Brackets
Brackets are another type of grouping tool in math. Similar to parentheses, they help prioritize operations. Typically, you solve expressions within brackets after addressing any parentheses inside them first.

Consider the expression: \[6-(2+3)\].
Here, we handled the parentheses \((2+3)\) to get the result 5, and then solved \(6-5\) inside the brackets, finding the result of 1.

Using brackets can make complex expressions easier to handle by breaking them into manageable parts.

Key points to remember:
  • Evaluate any parentheses within brackets first.
  • Simplify the expression inside just like any math problem.
Once simplified, it makes performing further operations straightforward.
Simplification Techniques
Simplification in math means breaking down expressions to their simplest form. This makes them easier to solve and understand. It involves clearing out unnecessary complexity, step by step, using the order of operations.

In the original exercise, the simplification process was:
  • Simplifying inside the parentheses: \((2+3)\).
  • Replacing and simplifying inside the brackets: \(6-5\).
  • Multiplying the result by any remaining operators: \(-8 \times 1\).
  • Finally, solve using basic arithmetic: \(9 - 8\).
Follow these sequences of operations to ensure consistent and accurate results each time.

Remember:
  • Simplification makes complex mathematics look simple.
  • It helps in making further calculations with ease.
So, always break down and simplify expressions wherever possible!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify the given expression. $$ \frac{60-(8 \cdot 6-3)}{5 \cdot 4-5} $$

Simplify the given expression. $$ 9 \cdot[3+4 \cdot(5+2)] $$

Use the distributive property to evaluate the given expression. $$ 6 \cdot(7-2) $$

Simplify the given expression. $$ 6+3 \cdot[4+4 \cdot(5+8)] $$

Simplify the given expression. $$ \frac{16+38}{6(3)} $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.