/*! 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 38 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 38

Simplify each expression. $$ 6-(9 y+5) $$

Short Answer

Expert verified
1 - 9y

Step by step solution

01

Distribute the negative sign

First, distribute the negative sign inside the parentheses. This means changing the sign of each term inside the parentheses.The expression becomes: \[6 - 9y - 5\]
02

Combine like terms

Next, combine the constant terms (numbers) in the expression. Combine 6 and -5:\[6 - 5 = 1\]So the expression simplifies to:\[1 - 9y\]

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.

Distribute the Negative Sign
Distributing a negative sign in an algebraic expression involves changing the signs of each term inside the parentheses. For instance, if you have an expression like 6-(9y+5), you start by distributing the negative sign across each term inside the parentheses.
In this case, the negative sign in front of the parentheses will turn +9y into -9y and +5 into -5.
Thus, the expression 6-(9y+5) simplifies to: 6 - 9y - 5.
Distributing negative signs correctly is crucial because any mistake here can lead to incorrect solutions.
Combine Like Terms
Combining like terms involves adding or subtracting terms that have the same variable part. In expression simplification, this usually means dealing with constants (numbers without variables) and terms containing the same variables.
In the expression 6 - 9y - 5, the like terms to combine are the constants 6 and -5. Combining them, you get:
6 - 5 = 1.
Therefore, the simplified expression becomes: 1 - 9y.
When combining like terms, ensure you only combine terms that have identical variable parts.
Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and mathematical operators (such as +, -, *, and /). These expressions can be simplified by following certain rules like distributing and combining like terms.
For example, consider the expression from the exercise: 6-(9y+5).
After distributing the negative sign and combining like terms, we simplified it to: 1 - 9y.
Understanding these rules and applying them correctly helps make complex expressions simpler and easier to work with. This skill is fundamental in algebra and is used in solving equations, factorizing expressions, and even in calculus.

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

When simplifying an expression, we usually do some steps mentally.Providing the property that justifies each statement in the given simplification. $$3 x+4+2 x+7$$ $$ =(3 x+4)+(2 x+7) $$

Solve each problem. The amount, in billions of dollars, that Americans spent on their pets from 2003 to 2016 can be approximated by substituting a given year for \(x\) in the following expression. $$2.493 x-4962$$ (Data from American Pet Products Manufacturers Association.) Find the amount spent in each year. Round answers to the nearest tenth. (a) 2003 (b) 2010 (c) 2016 (d) How did the amount Americans spent on their pets change from 2003 to \(2016 ?\)

Find each square root. If it is not a real number, say so. $$ -\sqrt{0.64} $$

Simplify each inequality if needed. Then determine whether the statement is true or false. $$ -11 \geq 0 $$

Complete the table of fraction, decimal, and percent equivalents. $$\begin{array}{|c|c|c|}\hline \begin{array}{c}\text { Fraction in Lowest Terms } \\\\\text { (or Whole Number) }\end{array} & \text { Decimal } & \text { Percent } \\\\\hline \frac{1}{10}& & \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.