/*! 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 152 Solve the equation. Round your a... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 152

Solve the equation. Round your answer to three decimal places, if necessary. $$44-9 x=61$$

Short Answer

Expert verified
The solution to the equation is \(x = -1.889\) when rounded to three decimal places.

Step by step solution

01

Move the term containing \(x\) to one side

First, isolate the term \(9x\) on one side of the equation. This can be done by adding \(9x\) to both sides of the equation to maintain equality. The equation then becomes: \(44 = 61 + 9x\).
02

Move the constants to the opposite side

Now, to isolate \(x\) completely, move the constant on the side of \(x\) to the other side. This can be achieved by subtracting \(61\) from both sides of the equation. The equation then changes to: \(44 - 61 = 9x\). Simplifying this gives: \(-17 = 9x\).
03

Solve for \(x\)

Finally, solve for \(x\) by dividing both sides by \(9\). This gives: \(x = -17 / 9\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Algebraic Equations
An algebraic equation is a statement of equality between two expressions formed by variables and constants using algebraic operations such as addition, subtraction, multiplication, and division. The purpose of solving these equations is to find the value of the unknown variable that makes the equation true.

For instance, in the provided exercise, we have the equation 44 - 9x = 61. This is a simple linear equation where the goal is to determine the value of x that will satisfy this condition of equality. The equation contains constants (44 and 61), a variable (x), and involves subtraction and multiplication operations.
The Process of Isolating the Variable
To determine the unknown in an algebraic equation, it's crucial to isolate the variable. This means that we want to get the variable by itself on one side of the equation, with all numerical values on the other side. This makes it clear what the variable equals.

In the given problem, the first step involved adding 9x to both sides to move it away from the constant 44. By doing so, we're applying the basic principle that whatever we do to one side of the equation, we must do to the other to maintain the balance. After rearranging the components, we get x alone on one side, specifically in the format of 9x = -17, where the lone x indicates isolation.
Techniques for Equation Simplification
Once we've worked towards isolating the variable, the next critical step is equation simplification. This means performing operations to simplify both sides of the equation as much as possible, ideally leaving the variable with a coefficient of 1.

In the exercise, after 9x has been isolated, we subtract 61 from 44 to get -17 = 9x. Here, simplification tells us that to get x by itself we should divide both sides by 9 since 9 is the coefficient of x. This division simplifies the right side to just x, and the left side to -17/9, which is the solution to the equation.

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Most popular questions from this chapter

Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=60^{\circ}$$

Determine whether the statement is true or false. Justify your answer. $$\cot ^{2} 10^{\circ}-\csc ^{2} 10^{\circ}=-1$$

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