/*! 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 3 Solve each equation for \(y\). ... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 3

Solve each equation for \(y\). $$M=\frac{1}{y}$$

Short Answer

Expert verified
y = \frac{1}{M}

Step by step solution

01

- Understand the Equation

The given equation is \( M = \frac{1}{y} \). We need to solve for \( y \).
02

- Isolate \( y \)

To isolate \( y \), we need to clear the fraction. Multiply both sides of the equation by \( y \) to get rid of the denominator: \( M \times y = 1 \).
03

- Solve for \( y \)

Now, solve for \( y \) by dividing both sides by \( M \): \( y = \frac{1}{M} \).

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. In algebra, symbols, often letters, represent numbers or other elements. These symbols and their operations follow specific rules, enabling us to solve equations like the one in this exercise.
For instance, in the equation given, variables such as M and y are used. This allows us to express relationships and solve for unknown values. Understanding algebra is crucial as it forms the foundation for higher mathematics. It also helps in various real-life applications, such as in engineering and science.
Isolating Variables
Isolating variables is a key step in solving equations. It involves manipulating the equation to get the variable of interest by itself on one side of the equation.
In the provided exercise, the goal is to solve for the variable y. The first step is to clear the fraction by multiplying both sides of the equation by y, resulting in: \[ M y = 1 \]
Next, to isolate y, divide both sides by M:\[ y = \frac{1}{M} \]
This process ensures y is alone on one side, giving the solution in terms of M. Isolating variables is essential in algebra as it simplifies equations and helps find solutions.
Fractions
Fractions represent parts of a whole and consist of a numerator (top part) and a denominator (bottom part). In equations, fractions can sometimes complicate the process of solving for a variable.
In the exercise, the fraction \[ \frac{1}{y} \] represents a relationship between M and y. To solve for y, we need to eliminate the fraction. This is done by multiplying both sides by y, converting the fraction into a simpler form: \[ M y = 1 \]
After this, solving for y involves straightforward division. Understanding how to handle fractions is fundamental in algebra, as it allows for the simplification and solving of various types of equations.

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Most popular questions from this chapter

Perform the indicated operations. $$\frac{x^{3}+1}{x^{2}-1} \cdot \frac{3 x-3}{x^{3}-x^{2}+x}$$

Either solve the given equation or perform the indicated operation \((s),\) whichever is appropriate. $$\frac{5}{h}-\frac{h}{5}$$

Solve each equation. $$\frac{5}{2 x+4}-\frac{1}{x-1}=\frac{3}{x+2}$$

Perform the indicated operations. Variables in exponents represent integers. $$\frac{x^{a}}{y^{2}} \cdot \frac{y^{b+2}}{x^{2 a}}$$

Solve each equation. $$\frac{x+4}{x^{3}+8}+\frac{x+2}{x^{2}-2 x+4}=\frac{11}{2 x+4}$$
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