/*! 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 98 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 98

Simplify each expression. $$ 5 w-2+4(w-3)-6(w-1) $$

Short Answer

Expert verified
3w - 8

Step by step solution

01

- Expand the expression

Begin by distributing the numbers outside the parentheses to simplify the expression. Distribute 4 to both terms in \(4(w-3)\) and -6 to both terms in \( -6(w-1)\). \[ 4(w-3) = 4w - 12 \] and \[ -6(w-1) = -6w + 6 \]. Now, rewrite the expression: \[ 5w - 2 + 4w - 12 - 6w + 6 \]
02

- Combine like terms

Combine the terms that contain \(w\) and the constant terms separately. The expression \[ 5w - 2 + 4w - 12 - 6w + 6 \] combines to \[ (5w + 4w - 6w) + (-2 - 12 + 6) \]. Simplifying these, \[(5 + 4 - 6)w = 3w\] and \[-2 - 12 + 6 = -8\]. Thus, the expression becomes \[ 3w - 8 \].

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 helps in breaking down complex algebraic expressions into simpler parts. It states that multiplying a number by a sum or difference is the same as multiplying that number by each term inside the parentheses and then adding or subtracting the results. This is written as:
For addition: a(b + c) = ab + ac.
For subtraction: a(b - c) = ab - ac.
In the provided exercise: 5w - 2 + 4(w - 3) - 6(w - 1)
We apply the distributive property as follows: 1. Distribute 4 across (w - 3) so it becomes: 4w - 12.
2. Distribute -6 across (w - 1) so it becomes: -6w + 6.
After these steps, the expression becomes: 5w - 2 + 4w - 12 - 6w + 6.
Combining Like Terms
After applying the distributive property, the next step is to simplify the expression by combining like terms. Like terms are terms that contain the same variables raised to the same power. Here, we look for terms involving 'w' and constant terms. In the expression: 5w - 2 + 4w - 12 - 6w + 6 We have:
  • Three terms with 'w': 5w, 4w, and -6w.
  • Three constant terms: -2, -12, and +6.
Combine the 'w' terms: 5w + 4w - 6w = 3w Combine the constant terms: -2 - 12 + 6 = -8 So, the simplified form of the expression becomes: 3w - 8
Algebraic Simplification
Algebraic simplification is the process of reducing an expression to its simplest form. This involves several steps like using the distributive property and combining like terms, as we have done above. The ultimate goal is to make the expression easier to work with by removing unnecessary complexity. For the expression given: 5w - 2 + 4(w - 3) - 6(w - 1) We used the distributive property: 4(w - 3) = 4w - 12 -6(w - 1) = -6w + 6 Next, we combined the like terms: 5w + 4w - 6w = 3w -2 - 12 + 6 = -8 Thus, the expression was simplified to: 3w - 8 By following these steps consistently, you can simplify any algebraic expression effectively. Remember:
  • Distribute first.
  • Combine like terms.
  • Always rewrite each step to avoid confusion.

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

Use an operation with signed numbers to solve each problem and identify the operation used. The Jones family has a house that is worth \(\$ 85,000,\) but they still owe \(\$ 45,000\) on the mortgage. They have \(\$ 2300\) in credit card debt, \(\$ 1500\) in other debts, \(\$ 1200\) in savings, and two cars worth \(\$ 3500\) each. What is the net worth of the Jones family?

Simplify each expression. $$ (-3 x+4)-(6 x-6) $$

Find each product or quotient. $$ \frac{-x t+10}{-2} $$

Writing What is the difference between a rational and an irrational number? Why is \(\sqrt{9}\) rational and \(\sqrt{3}\) irrational?

Find each product or quotient. $$ (-2 x)(-5 x) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.