/*! 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 49 Find each product. $$ -1(3 x... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 49

Find each product. $$ -1(3 x-2) $$

Short Answer

Expert verified
-3x + 2

Step by step solution

01

Distribute -1

Distribute the -1 to each term inside the parentheses. This means multiplying -1 by each term in the parentheses \[ -1(3x-2) = (-1) \times (3x) + (-1) \times (-2) \]
02

Multiply -1 by each term

Multiply -1 by 3x to get -3x and multiply -1 by -2 to get +2 \[ -1 \times 3x = -3x \ -1 \times -2 = +2 \]
03

Combine the results

Put the results of the multiplications together \[ -3x + 2 \]

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 a combination of variables, numbers, and operations (like addition and multiplication). They can be simple, like \(3x\), or more complex, like \(3x - 2\). When we talk about algebraic expressions, it's important to understand each part:
  • Variables: Symbols (usually letters) that represent unknown values. In our example, \(x\) is the variable.
  • Coefficients: Numbers that are multiplied by variables. For instance, \(3\) in \(3x\).
  • Constants: Fixed numbers that stand alone, like \(-2\) in our example.
Understanding these components helps in recognizing how operations affect the expression.
Multiplication
When we multiply in algebra, we often use the distributive property to break down expressions. The distributive property states that \(a(b + c) = ab + ac\). This means we need to multiply each term inside the parentheses by the term outside. Let's see how this works with the example \(-1(3x - 2)\):
  • Step 1: Distribute -1: Multiply \(-1\) by each term inside the parentheses. This gives us \((-1) \times (3x) + (-1) \times (-2)\).
  • Step 2: Multiply: Solve the multiplications \(-1 \times 3x = -3x\) and \(-1 \times -2 = +2\).
We multiply numbers first, then the variables, and finally combine all parts.
Simplifying Equations
Simplifying equations involves reducing them to the simplest form. After we multiply, we combine like terms to clean up the expression. Let's continue with our exercise:
  • Step 1: Combine Like Terms: We see we have \(-3x\) and \(+2\) left. Since they are different types (one with \(x\) and one constant), they can't be combined further.
  • Result: The simplified form of \(-1(3x - 2)\) is \(-3x + 2\).
Simplifying helps make equations easier to understand and solve.

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

If you divide each side of \(x^{2}=x\) by \(x,\) you get \(x=1\) If you subtract \(x\) from each side of \(x^{2}=x,\) you get \(x^{2}-x=0,\) which has two solutions. Which method is correct? Explain.

Factor each polynomial using the trial-and-error method. $$ a^{2}+a-30 $$

Factor each polynomial using the trial-and-error method. $$ x^{2}+10 x+21 $$

Factor each polynomial by grouping. $$ a x-2 a+4 x-8 $$

Solve each equation for \(y .\) Assume a and b are positive numbers. $$4 y^{2}+4 b y+b^{2}=0$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

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.