Solve the equation. Check your solutions. (5)/(2 y)=(7)/(y-3)

Name: Problem 29, Chapter 11: Algebra 1: Concepts and Skills
Uploaded: 2020-04-22T14:36:22-08:00
Duration: 1 min 8 s
Channel: Julie Silva
Description: Solve the equation. Check your solutions. (5)/(2 y)=(7)/(y-3)

step 1 We're being asked to solve the given equation. Well, because it's a proportion, I'm going to do

Solve the equation. Check your solutions. (5)/(2...

Key Concepts

Rational Equations

Rational equations are equations that involve one or more rational expressions—fractions where the numerator and/or denominator contain algebraic expressions. They require careful manipulation to account for the presence of variables in the denominator and often involve techniques to combine, simplify, or eliminate these fractions to solve for the unknown.

Domain Restrictions

When working with rational equations, it is essential to identify restrictions on the variable that arise from denominators. Specifically, any value that makes a denominator zero must be excluded from the solution set. This step prevents arriving at solutions that are not valid in the context of the original equation.

Cross Multiplication

Cross multiplication is a technique commonly used when an equation sets two fractions equal to each other. By multiplying across the equality (i.e., multiplying the numerator of one fraction by the denominator of the other), the equation is transformed into one without denominators. This method offers a straightforward way to solve the equation but must be applied carefully with attention to domain restrictions.

Extraneous Solutions

Extraneous solutions are potential answers obtained during the process of solving equations that, when substituted back into the original equation, lead to undefined expressions, such as division by zero, or do not satisfy the original equation. Checking each solution by substituting it back is critical to ensure that only valid solutions are accepted.

Solution Verification

Solution verification is the process of substituting the obtained solutions back into the original equation to confirm they do not produce any contradictions or violations, such as division by zero. This step is crucial, especially in rational equations, to ensure mathematical validity and to identify any extraneous solutions.

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