Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 124

Chapter 3, Problem 124

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y : x = 5/y + 4

Verified step by step guidance

Start by isolating the term containing y. Subtract 4 from both sides of the equation to get: x - 4 = 5/y.

To eliminate the fraction, multiply both sides of the equation by y. This gives: y(x - 4) = 5.

Next, divide both sides of the equation by (x - 4) to isolate y. This results in: y = 5 / (x - 4).

Ensure that the denominator (x - 4) is not equal to zero, as division by zero is undefined. Check the condition: x ≠ 4.

The solution for y is expressed as y = 5 / (x - 4), with the restriction that x ≠ 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solving Equations

Solving equations involves finding the value of a variable that makes the equation true. In this case, we need to isolate 'y' in the equation x = 5/y + 4. This process often requires algebraic manipulation, such as moving terms from one side of the equation to the other and performing operations like multiplication or division.

Rational Expressions

A rational expression is a fraction where the numerator and/or denominator are polynomials. In the equation given, 5/y is a rational expression. Understanding how to manipulate rational expressions, including finding a common denominator and simplifying, is crucial for solving equations that involve them.

Inverse Operations

Inverse operations are pairs of operations that undo each other, such as addition and subtraction or multiplication and division. To solve for 'y', we will use inverse operations to isolate 'y' on one side of the equation. Recognizing which operations to apply is essential for effectively solving algebraic equations.

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Simplify: $2 (x + h)^{2} + 3 (x + h) + 5 - (2 x^{2} + 3 x + 5)$ .