/*! 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 41 Solve. $$ 7 x-5=-54 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 41

Solve. $$ 7 x-5=-54 $$

Short Answer

Expert verified
The solution is \(x = -7\).

Step by step solution

01

Add 5 to Both Sides

To isolate terms involving \(x\), we start by adding 5 to both sides of the equation. This gives us:\[7x - 5 + 5 = -54 + 5\]which simplifies to:\[7x = -49\]
02

Divide by 7

Next, we divide both sides of the equation by 7 to solve for \(x\):\[\frac{7x}{7} = \frac{-49}{7}\]This simplifies to:\[x = -7\]

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.

Understanding Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In algebra, we often use letters to represent numbers. This can help us form equations and solve various types of problems.

Algebra is like a language that allows us to describe mathematical ideas more generally. Think of it as a toolkit that lets us solve problems efficiently. When working with algebraic equations, you may often use:
  • Variables: Letters like \(x\) or \(y\) that stand in for unknown numbers.
  • Constants: Numbers that are always the same, like 5 or -2.
  • Operations: Actions like addition, subtraction, multiplication, and division.
These components together allow us to formulate equations and solve for unknowns. Once you grasp the basics of algebra, it becomes much easier to handle more complex mathematical problems.
Mastering the Art of Solving Equations
Solving equations is a fundamental skill in algebra. It involves finding the value of a variable that makes an equation true. The key to solving equations is to perform operations that simplify the equation step by step until the variable is isolated.

Here is a simple guideline to solve equations:
  • Keep the equation balanced by performing the same operations on both sides.
  • Simplify progressively. Start by getting rid of constants on one side.
  • Once you've isolated the term with the variable, solve for the variable by performing the reverse operation.
Imagine your equation as a balance scale. Whatever you do to one side, you must do to the other to maintain balance. This approach helps in reaching the correct solution systematically, as we saw in the original exercise.
Isolation of Variable
Isolation of the variable is a critical step in solving any equation. This means getting the variable by itself on one side of the equation. The main goal is to simplify the equation to the form where the variable equals a number.

Let's break down the steps on how to isolate a variable:
  • To begin with, remove any constants from the side of the equation containing the variable. For example, in the equation \(7x - 5 = -54\), you would add 5 to both sides.
  • Next, eliminate any coefficients attached to the variable by performing the inverse operation. In this case, divide both sides of the equation by the coefficient of \(x\), which is 7.
After performing these operations, you should reach a point where the variable, such as \(x\), stands alone on one side, making it easy to see its value in the equation.

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

Determine the inequality given the answers expressed in interval notation. $$ (-\infty, 1) \cup[3, \infty) $$

The length of a rectangle is 7 centimeters less than twice its width. If the perimeter measures 46 centimeters, then find the dimensions of the rectangle.

Solve and graph the solution set. In addition, present the solution set in interval notation. $$ 3 x-7<14 \text { or } 2 x+3>7 $$

The ratio of female to male employees at a certain bank is 4 to 5 . If there are 80 female employees at the bank, then determine the total number of employees.

Graph all solutions on a number line and provide the corresponding interval notation. $$ x>-2 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.