/*! 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 1 Solve the equation. $$-3 x+4=-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 1

Solve the equation. $$-3 x+4=-1$$

Short Answer

Expert verified
The solution is \(x = \frac{5}{3}\).

Step by step solution

01

Isolate the Variable Term

First, we want to get all terms involving the variable on one side of the equation and constant terms on the other side. We start by subtracting 4 from both sides of the equation to isolate the term with \(x\).\[-3x + 4 - 4 = -1 - 4\]This simplifies to:\[-3x = -5\]
02

Solve for the Variable

Now, we need to solve for \(x\). Since \(-3x\) means \(-3\) times \(x\), we divide both sides of the equation by \(-3\) to get \(x\) by itself.\[\frac{-3x}{-3} = \frac{-5}{-3}\]This simplifies to:\[x = \frac{5}{3}\]

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.

Solving Equations
Equations are like balanced scales. Both sides must remain equal. When solving equations, the goal is to find the value of a variable, often represented as \(x\), that makes the equation true. We do this by performing operations that maintain the balance.
  • Begin by simplifying each side of the equation if needed, such as removing parentheses or combining like terms.
  • Ensure all terms with the variable are on one side and constants on the other. This often involves adding, subtracting, multiplying, or dividing.
  • Perform the same operation on both sides to maintain equality. Be mindful of inverse operations which undo what's being done to the variable.
Solving step-by-step helps eliminate mistakes. It ensures clarity and correct results while making each process straightforward to follow.
Isolation of Variable
When solving equations, one key step is the isolation of the variable. This means getting the variable by itself on one side of the equation. In our example, we isolate \(x\) by moving other terms to the opposite side while keeping the balance of the equation.
  • Subtract or Add: Use addition or subtraction to move constants away from the variable. In the equation \(-3x + 4 = -1\), subtracting 4 from both sides helped isolate the \(x\) term.
  • Division or Multiplication: If the variable is multiplied by a number, use division to isolate it. If divided, use multiplication.
Moving terms across the equation is like shifting weight on a balance scale; you need to keep both sides equal to maintain correctness.
Step-by-Step Solution
A step-by-step solution improves understanding by breaking down the problem-solving process into manageable parts. This helps to pinpoint errors quickly and make complex equations seem more approachable. Let's unpack the process used in the example step-by-step:
  • Identify Required Operations: Identify what needs isolation, in this case, the \(x\). Look at the operations involved, such as addition, subtraction, and division, to determine how to proceed.

  • Execute Each Step Rigorously: Take each identified step carefully. Subtract 4 from both sides, then divide by \(-3\). Each operation is critical to isolating the variable.

  • Verify Your Answer: After solving, substitute back into the original equation to verify the solution is correct. This ensures the step-by-step approach led to the right results.
Step-by-step solving not only fosters better comprehension but also instills confidence in problem-solving.

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

Show that the equation is an identity. $$\frac{49 x^{2}-25}{7 x-5}=7 x+5$$

Solve the equation. $$\frac{3}{y}+\frac{6}{y}-\frac{1}{y}=11$$

The formula occurs in the indicated application. Solve for the specified variable. \(R=\frac{V}{I}\) for \(I\)

A worker's take-home pay is \(\$ 492\), after deductions totaling \(40 \%\) of the gross pay have been subtracted. What is the gross pay?

A water tank can be emptied by using one pump for 5 hours. A second, smaller pump can empty the tank in 8 hours. If the larger pump is started at 1:00 P.M., at what time should the smaller pump be started so that the tank will be emptied at 5:00 P.M.?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Geometry

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.