/*! 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 81 Remove parentheses and simplify.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 81

Remove parentheses and simplify. $$ 2 p-(7-4 p) $$

Short Answer

Expert verified
6p - 7

Step by step solution

01

Distribute the negative sign

First, we need to remove the parentheses by distributing the negative sign through the expression inside the parentheses. This means we will change the sign of each term inside the parentheses: (7 - 4p) becomes -7 + 4p.
02

Rewrite the expression

Now, rewrite the original expression with the distributed terms: 2p - (7 - 4p) becomes 2p - 7 + 4p.
03

Combine like terms

Combine the like terms (the terms with p) together to simplify the expression: 2p + 4p = 6p. Therefore, the expression now becomes 6p - 7.

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 a useful tool when dealing with algebraic expressions. It allows us to simplify expressions involving parentheses by distributing a factor across terms inside the parentheses. This property is often written as: \[a(b + c) = ab + ac\]In our example, we used the distributive property with a negative sign to simplify the expression 2p - (7 - 4p).
Here's how we did it:
  • We treated the negative sign as -1 and distributed it to each term inside the parentheses. So, (7 - 4p) became -7 + 4p.
  • This step is crucial as it changes the signs of the terms within the parentheses.
By understanding and applying the Distributive Property, we can easily handle expressions with parentheses and prepare for further simplification.
Combining Like Terms
Combining like terms is an essential skill in algebra. It helps us to simplify expressions by merging terms that have the same variable with the same exponent. Like terms in an expression can be combined by adding or subtracting their coefficients.

For example, in the expression 2p - 7 + 4p, we have two terms that include the variable 'p': 2p and 4p.
  • We add the coefficients of these like terms: 2 and 4, and get 6.
  • So, 2p + 4p simplifies to 6p.
After combining like terms, the expression becomes 6p - 7.

Combining like terms helps to streamline algebraic expressions and makes solving equations much simpler.
Removing Parentheses
Removing parentheses is often the first step in simplifying algebraic expressions. This is achieved by using the distributive property or by recognizing that the parentheses can be eliminated when no operation is needed inside them.

In our example, 2p - (7 - 4p), we used the negative sign outside the parentheses to distribute it to each term inside:
  • The expression inside the parentheses, (7 - 4p), was changed to -7 + 4p.
By removing the parentheses correctly, we obtain a simplified version of the expression.Understanding how to remove parentheses properly is a fundamental step in algebra, enabling us to simplify and solve complex expressions logically.

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

Solve each system using the elimination method. $$ \begin{aligned} &3 x+y=-1\\\ &2 x-3 y=-8 \end{aligned} $$

Combine like terms. $$ -6 x+7+9 x $$

Solve each system using the substitution method. $$ \begin{aligned} &a-2 b=3\\\ &3 a=6 b+9 \end{aligned} $$

Determine whether the given number is a solution of the given equation. $$ 144 ; \frac{x}{9}=16 $$

Multiply. $$ -3(2 x-y+z) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Pure 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.