/*! 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 62 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 62

Simplify each expression. $$ 4(6 y-9)+7 $$

Short Answer

Expert verified
24y - 29

Step by step solution

01

- Distribute the 4

First distribute the 4 to both terms inside the parentheses. This means multiplying 4 by each term: \[ 4 \times 6y - 4 \times 9 + 7 \]
02

- Multiply

Now perform the multiplication: \[ 24y - 36 + 7 \]
03

- Combine like terms

Combine the constants -36 and 7: \[ 24y - 29 \]

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.

distribution in algebra
Distribution in algebra is a method used to simplify expressions where you multiply a single term by two or more terms inside parentheses. It applies the distributive property which states: \[ a(b + c) = ab + ac \]. In our exercise, we distributed the number 4 to both terms inside the parentheses, \(6y - 9\). This resulted in: \[ 4 \times 6y - 4 \times 9 \]. Distribution helps in breaking down complex expressions into simpler ones, making them easier to solve.

Example: \(3(x + 5) = 3x + 15\).
Trust the process! Breaking down each step will lead you to the correct simplification.
combining like terms
Combining like terms is an essential step in simplifying algebraic expressions. Like terms are terms that contain the same variables raised to the same power. In our solution, after distribution and multiplication, we had: \[ 24y - 36 + 7 \]. Here, \(24y\) is one term, and \(-36 + 7\) are the constants. To combine like terms, you simply add or subtract their coefficients:

\textbullet Combine \(-36 + 7\) to get \(-29\).
This gives the simplified expression: \[ 24y - 29 \].
It's like grouping together similar items to make them easier to count. Always make sure that only like terms are combined!
algebraic multiplication
Algebraic multiplication involves multiplying numbers and variables. It appears in various algebraic operations but is crucial in the distribution step. In our problem, multiplication was performed twice: \[ 4 \times 6y \] and \[ 4 \times 9 \]. Let鈥檚 break it down:

\textbullet The term \((4 \times 6y)\) simplifies to \((24y)\), because you multiply the constants first and keep the variable.

\textbullet The term \((4 \times 9)\) simplifies to \((36)\).
Understanding how to multiply expressions accurately is key. Always multiply the coefficients and follow the rules of combining any like variables properly. Master these skills, and you'll excel in simplifying algebraic expressions!

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

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by 9 and (b) \(2,287,321\) is not divisible by \(9 .\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (5 x-2 y)(-2 a) $$

Write a numerical expression for each phrase and simplify. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 3 is \(-3\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 3 if the sum of its digits is divisible by \(3,\) and not otherwise. Show that (a) \(4,799,232\) is divisible by 3 and (b) \(2,443,871\) is not divisible by 3
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.