Question

Solve each proportion. $$ \frac{2}{x+6}=\frac{-2 x}{5} $$

   Solve each proportion.
$$
\frac{2}{x+6}=\frac{-2 x}{5}
$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 7, Problem 58

Instant Answer

Solved by Expert Ali Soave

04/02/2020

Step 1

Step 1: Cross multiply the given equation to get rid of the fractions: $$ 2(5) = -2x(x+6) $$ This simplifies to: $$ 10 = -2x^2 - 12x $$ Show more…

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Solve each proportion. $$ \frac{2}{x+6}=\frac{-2 x}{5} $$

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Key Concepts

Solving Quadratic Equations

Often, after cross multiplying in a proportion, the resulting equation is quadratic. Solving quadratic equations involves techniques such as factoring, completing the square, or using the quadratic formula. This process is a key tool in algebra and critical for finding all possible solutions to the equation.

Rational Equations and Domain Restrictions

Rational equations are equations that involve fractions where the numerator and/or denominator are algebraic expressions. A critical aspect of handling these equations is ensuring that any restrictions on the variable are observed, specifically that denominators cannot be zero. Identifying these restrictions is an essential part of solving the equation correctly.

Proportions

A proportion is an equation that states that two ratios are equivalent. In solving proportions, the goal is to find the value of the variable that makes the two fractions equal. This concept is fundamental in various areas of algebra and is used to solve problems involving scaling and comparisons.

Cross Multiplication

Cross multiplication is a technique used to eliminate the fractions in a proportion by multiplying the numerator of each fraction by the denominator of the other. This method simplifies the problem into a form that is easier to solve, typically resulting in a linear or quadratic equation.

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