/*! 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 16 Solve each equation. $$5(x+3)+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 16

Solve each equation. $$5(x+3)+4 x-3=-(2 x-4)+2$$

Short Answer

Expert verified
x = -\frac{6}{11}

Step by step solution

01

- Distribute and Simplify

Distribute the 5 on the left side:\[5(x + 3) + 4x - 3 = 5x + 15 + 4x - 3\]Combine like terms:\[9x + 12\]On the right side, distribute the negative sign:\[-(2x - 4) + 2 = -2x + 4 + 2\]Combine like terms:\[-2x + 6\]Now the equation is:\[9x + 12 = -2x + 6\]
02

- Move Variables to One Side

Add \(2x\) to both sides to move all \(x\) terms to one side:\[9x + 12 + 2x = -2x + 6 + 2x\]Simplify:\[11x + 12 = 6\]
03

- Solve for x

Subtract 12 from both sides to move constants to the right side:\[11x + 12 - 12 = 6 - 12\]Simplify:\[11x = -6\]Divide both sides by 11 to solve for \(x\):\[x = \frac{-6}{11}\]

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 key principle in algebra. It allows you to multiply a number by a sum or difference inside a set of parentheses. For instance, in the equation \(5(x + 3)\), you would distribute 5 to both \(x\) and 3. So, this becomes:
\(5(x + 3) = 5x + 15\).
This is helpful because it simplifies the equation, making it easier to solve. Always perform the distribution for every term inside the parentheses.
Combining Like Terms
When solving linear equations, combining like terms is essential. Like terms are terms that have the same variable raised to the same power. For example:
Combining terms in the expression \(5x + 15 + 4x - 3\) yields:
\(5x + 4x\) (both have the variable \(x\)) and \(15 - 3\) (both are constants).
Simplifying, this becomes:
\(9x + 12\).
Combining like terms makes equations simpler and more manageable.
Isolating Variables
Isolating variables means getting the variable you are solving for on one side of the equation. This is done so that you can solve the equation for that variable. In our example, after combining like terms, we have:
\(9x + 12 = -2x + 6\).
To isolate \(x\), add \(2x\) to both sides:
\(9x + 12 + 2x = -2x + 6 + 2x\), which simplifies to \(11x + 12 = 6\).
Then, move the constant term by subtracting 12 from both sides:
\(11x + 12 - 12 = 6 - 12\), which simplifies to \(11x = -6\).
Finally, divide by 11 to isolate \(x\):
\(x = \frac{-6}{11}\).
Basic Algebra
Basic algebra involves understanding and applying foundational concepts like variables, constants, and operations (addition, subtraction, multiplication, and division). When solving equations, follow these steps:
  • Distribute constants.
  • Combine like terms.
  • Isolate the variable.
  • Simplify your answer.

Practicing these steps will help you solve equations more effectively and build a strong mathematical foundation.

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 problem. The industrial process that is used to convert methanol to gasoline is carried out at a temperature range of \(680^{\circ} \mathrm{F}\) to \(780^{\circ} \mathrm{F}\). Using \(F\) as the variable, write an absolute value inequality that corresponds to this range.

Solve each rational inequality. Write each solution set in interval notation.4 $$\frac{(5-3 x)^{2}}{(2 x-5)^{3}}>0$$

Sohe each equation or inequality. \(|4.3 x+9.8|<0\)

Simplify each power of i. $$i^{-13}$$

Write each statement as an absolute value equation or inequality. \(k\) is within 0.0002 unit of \(10 .\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied 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.