/*! 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 71 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 71

Simplify each expression. $$ 6-(x-4) $$

Short Answer

Expert verified
\(10 - x\)

Step by step solution

01

Understand the Expression

The expression given is \(6-(x-4)\). Note that the subtraction of \((x-4)\) must be distributed correctly.
02

Distribute the Negative Sign

Distribute the negative sign inside the parentheses: \(6 - (x - 4) = 6 - x + 4\). This turns \(- (x - 4)\) into \(-x + 4\).
03

Combine Like Terms

Combine the constants \(6\) and \(4\) to simplify the expression: \(6 - x + 4 = 10 - x\).

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.

Distributive Property
The distributive property is an important concept in algebra. It tells us how to multiply a number by a sum or difference inside parentheses.
To put it simply, if you see an expression like \(a(b + c)\), you should distribute \(a\) to both \(b\) and \(c\).
So, \(a(b + c) = ab + ac\). This property holds for subtraction too. For instance, \(a(b - c) = ab - ac\).

In our exercise, we use the distributive property to handle the negative sign before the parentheses. By distributing the negative sign, we ensure that both terms inside change signs as necessary.
Combining Like Terms
Combining like terms means simplifying an expression by summing up terms that have the same variable.
For instance, in the expression \(3x + 5x - 2\), you can combine \(3x\) and \(5x\) to get \(8x\). This leaves the simplified expression as \(8x - 2\).

In our example, after distributing the negative sign, the expression looks like \(6 - x + 4\). Here, \(6\) and \(4\) are constants (numbers without variables), and \(-x\) is a term with a variable.
So, we combine \(6\) and \(4\) to get \(10\), giving us \(10 - x\).
Negative Sign Distribution
When you have a negative sign in front of parentheses, it means you need to distribute it to all terms inside the parentheses.
Consider the exercise expression \(6 - (x - 4)\). You can think of the negative sign as a \(-1\).
So, distributing it inside gives us \(-x + 4\), changing each term's sign inside the parentheses.

This makes our expression \(6 - x + 4\). Always pay close attention to the signs while distributing, as missing it can lead to incorrect results.
By mastering this, you can simplify expressions accurately!

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

Write an algebraic expression for each problem. Parallelogram. The lengths of the sides of a lot in the shape of a parallelogram are \(w\) feet and \(w+50\) feet. What is its perimeter? Is it possible to find the area from this information?

Evaluate each radical. $$\sqrt{49}$$

Combine like terms. $$ -5 x-(-2 x) $$

After reading this section, write out the answers to these questions. Use complete sentences. Why are grouping symbols used?

Evaluate each expression. $$2^{4}-4^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

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.