Solve each proportion. (3 x-1)/(2)=(-2)/(x+2)

Name: Problem 25, Chapter 7: Geometry
Uploaded: 2020-06-18T18:58:26-08:00
Duration: 2 min 15 s
Channel: Ashley High
Description: Solve each proportion. (3 x-1)/(2)=(-2)/(x+2)

Key Concepts

Proportions

A proportion is an equation where two ratios or fractions are set equal to each other. Understanding proportions is essential in algebra as it involves comparing relationships between quantities. This concept is foundational and applies across various problems, allowing for the determination of unknown values by using the equivalence of ratios.

Rational Equations

A rational equation involves expressions that contain ratios of polynomials. These types of equations require careful handling because the variables appear in the denominators, which may restrict the domain. Recognizing a rational equation is key to applying techniques that not only solve for the variable but also ensure that the proposed solutions do not result in an undefined expression.

Cross Multiplication

Cross multiplication is a straightforward method used to solve proportions. When two fractions are equal, their cross products are also equal. This technique simplifies the process of solving equations by eliminating the denominators and converting the proportion into a basic algebraic equation, which can then be solved using standard methods.

Extraneous Solutions and Domain Restrictions

When solving equations that include variables in the denominator, it is important to check for extraneous solutions. These are solutions that might be mathematically derived but do not satisfy the original condition because they make a denominator zero. This concept highlights the importance of considering domain restrictions when working with rational equations to ensure that the final answers are valid within the context of the problem.

Transcript

Please give Ace some feedback