/*! 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 120 Solve by graphing. $$ x-1=-5... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 120

Solve by graphing. $$ x-1=-5 $$

Short Answer

Expert verified
\( x = -4 \).

Step by step solution

01

Identify the equation

The given equation is \( x - 1 = -5 \).
02

Solve for x

Add 1 to both sides of the equation to isolate \( x \).\( x - 1 + 1 = -5 + 1 \)This simplifies to \( x = -4 \).
03

Graph the equation

Plot the point where \( x = -4 \) on the x-axis. This is a vertical line crossing the x-axis at \( -4 \). Locate \( -4 \) on a number line and draw a point there.

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
Solving equations is a foundational skill in algebra that requires finding the value of the variable that makes the equation true. In our original exercise, we are given the equation:

\[ x - 1 = -5 \].
To solve this, we need to isolate the variable on one side of the equation. The steps involve performing arithmetic operations to both sides to maintain equality. To solve for \( x \), we identify and execute the following step:

  • Add 1 to both sides to cancel out the -1 on the left-hand side:
  • \[ x - 1 + 1 = -5 + 1 \] which simplifies to \[ x = -4 \].

Now, you have found that \( x = -4 \) is the solution that balances the original equation.
Graphing Linear Equations
Graphing linear equations is a way to visually represent solutions on the coordinate plane. For the equation

\[x - 1 = -5\],

we have determined from the previous steps that the value of \(x\) is -4. To graph this:

  • Locate -4 on the x-axis.
  • Draw a point at -4 and it represents the solution \(x = -4\).
For this specific type of equation, it will appear as a vertical line crossing through the x-axis at -4 since the solution for \(x\) is constant regardless of the value of \(y\). This helps in visualizing that all points on this line share the same x-coordinate (-4).
Isolation of Variables
Isolation of variables is a crucial step in solving algebraic equations, where you manipulate the equation to have the variable of interest alone on one side. In the problem \(x - 1 = -5\), to isolate \(x\), you perform the following steps:

  • Identify the operation that is affecting the variable (here it is -1).
  • Apply the inverse operation to both sides to cancel out the effect (adding 1 to both sides in this case).
  • \[ x - 1 + 1 = -5 + 1 \] simplifies to \[ x = -4 \]

This method ensures the variable is isolated, making it easier to determine its value. When isolating variables, always perform the same operation on both sides to keep the equation balanced and do the opposite of what is currently applied to the variable (addition cancels subtraction, and vice versa). This consistent approach can be applied to solve more complex algebraic equations as well.

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

Classify each of the following statements as either true or false. \(|x|\) is never negative.

Determine whether each ordered pair is a solution of the given inequality. $$ (3,-6) ; 4 x+2 y \leq-2 $$

Solve. $$ |y|=7.3 $$

Match each equation or inequality with an equivalent statement from the column on the right. Letters may be used more than once or not at all. $$ |x-3|>-5 $$ a) The solution set is \(\varnothing .\) b) The solution set is \(\mathbb{R}\). c) \(x-3>5\) d) \(x-3<-5\) or \(x-3>5\) e) \(x-3=5\) f) \(x-3<5\) g) \(x-3=-5\) or \(x-3=5\) h) \(-5

Solve. $$ |x-6|=1 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.