/*! 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 96 Write each expression without pa... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 96

Write each expression without parentheses. $$ -(-z+5 w-9 y) $$

Short Answer

Expert verified
z - 5w + 9y

Step by step solution

01

Identify the Expression

The given expression is \(-(-z + 5w - 9y)\)
02

Distribute the Negative Sign

Apply the negative sign located outside the parentheses to each term within the parentheses. Recall that \(-(-a) = a\), so: \[-(-z + 5w - 9y) = z - 5w + 9y\]

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.

Algebraic Expressions
Algebraic expressions are mathematical phrases that can include numbers, variables (like \(z\), \(w\), \(y\)), and operations (such as addition, subtraction, multiplication, and division). They are used to represent relationships between quantities and can be simplified or evaluated given certain values for the variables. In this exercise, we work with an algebraic expression that involves parentheses and needs to be rewritten without them.
Negative Sign Distribution
One key concept to grasp for this type of exercise is the distribution of a negative sign across terms inside parentheses. To distribute a negative sign, multiply each term inside the parentheses by -1. This process changes the sign of each term.

For example, in the expression \(-(-z + 5w - 9y)\), we distribute the negative sign across each term within the parentheses:
  • The negative outside and the negative \(z\) become positive \(z\): \(-(-z) = z\).
  • The negative outside and the positive \(5w\) become negative \(5w\): \(-(5w) = -5w\).
  • The negative outside and the negative \(9y\) become positive \(9y\): \(-(-9y) = 9y\).

So, the expression \(-(-z + 5w - 9y)\) simplifies to \(z - 5w + 9y\).
Simplifying Expressions
Simplifying expressions is an essential skill in algebra. It involves combining like terms and eliminating parentheses to make the expression more compact and easier to work with.

In our example, the initial expression is \(-(-z + 5w - 9y)\). By distributing the negative sign, we change each term inside the parentheses and remove the parentheses.

The process simplifies the expression to \(z - 5w + 9y\). This rewritten form is simpler and still has the same meaning as the original expression. Simplified expressions are more straightforward to use in further calculations, making problem-solving easier.

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 each expression without parentheses. $$ -(9 x+12 y) $$

Write a numerical expression for each phrase, and simplify the expression. 12 less than the difference of 8 and -5

Solve each problem. Based on 2020 population projections, Illinois will probably lose 2 seats in the U.S. House of Representatives, Minnesota will lose 1 seat, and New York will lose 1 . Write a signed number that represents the total number of seats these three states are projected to lose. (Data from Election Data Services.)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\frac{5 y^{2}+4}{x}\)

Use the distributive property to rewrite each expression. $$ -3(2 x-5) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.