/*! 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 21 Write each expression without us... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 21

Write each expression without using a multiplication symbol or parentheses. $$ 4 \cdot x $$

Short Answer

Expert verified
4x

Step by step solution

01

Understand the Expression

The given expression is \(4 \cdot x\), which means 4 multiplied by x. Our goal is to rewrite it without using the multiplication symbol (\(\cdot\)) or any parentheses.
02

Use the Variables and Numbers Together

When multiplying a number by a variable, it can be simplified by writing the number directly next to the variable. This is a standard mathematical convention where both are understood to be multiplied together. So \(4 \cdot x\) becomes \(4x\).

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 Mathematical Conventions
Mathematical conventions serve as a universal language for mathematicians worldwide. They allow us to convey mathematical ideas efficiently and unambiguously. In the context of algebraic expressions, a significant convention is the way we represent multiplication. When we have an expression like \(4 \cdot x\), instead of using the multiplication symbol, we can simply write \(4x\).
This approach eliminates the need for symbols and keeps expressions tidy and concise.

Other mathematical conventions that you may come across include:
  • Writing variables next to each other, like \(xy\) for \(x \cdot y\).
  • Understanding that numbers and variables written together imply multiplication.
These conventions are not just about neatness but are essential for communicating complex ideas in a simplified manner.
Simplifying Expressions
Simplifying expressions is a foundational skill in algebra. This process involves reducing mathematical expressions to their simplest form, making them easier to work with.
For instance, consider \(4 \cdot x\). Following mathematical conventions, we can simplify this to \(4x\). This process removes clutter such as multiplication symbols or parentheses that are not needed.

The process of simplifying an expression often includes:
  • Combining like terms, such as \(3x + 4x\) to \(7x\).
  • Eliminating redundant components, like unnecessary brackets.
  • Applying basic arithmetic operations to consolidate terms further.
Learning to simplify expressions efficiently improves your problem-solving skills and helps you tackle more complex algebraic problems with ease.
Using Mathematical Notation
Mathematical notation is a powerful tool, providing a standardized method of communication between mathematicians around the world. It comprises symbols, letters, and numbers to represent mathematical concepts succinctly.
In our given problem, the expression \(4 \cdot x\) is simplified using notation by writing \(4x\).

Here are some aspects of mathematical notation that help in its effectiveness:
  • It allows for the compact representation of complex ideas, reducing lengthy verbal explanations.
  • Provides clarity by removing potential ambiguities, as long as mathematical rules are followed precisely.
  • Enables mathematicians to share their findings without language barriers.
Mastery of mathematical notation not only aids in simplifying individual expressions but also enhances overall analytical skills and understanding of math.

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 each expression, if possible. $$ -6(3 t-6)-3(11 t-3) $$

Simplify each expression, if possible. $$ 70 a \cdot 10 $$

Simplify each expression, if possible. $$ 5 t \cdot 60 $$

Suppose \(a\) is a positive number and \(b\) is a negative number. Determine whether the given expression is positive or negative. a. \(-a(-b)\) b. \(\frac{-a}{b}\) c. \(\frac{-a}{a}\) d. \(\frac{1}{b}\)

Law Enforcement. A burglar scored \(-18\) on a lie detector test, a score that indicates deception. However, on a second test, he scored \(+3,\) a score that is inconclusive. Find the change in the scores.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.