Question

table of contents > module 7: rational expressions and equations > module 7 pretest: rational expressions and equations module 7 pretest: rational expressions and equations score: 5/9 answered: 5/9 question 6 solve the equation \\(\frac{-8}{7x} = \frac{1}{9x + 2}\\) \\(x = \square\\) (if needed, enter your answer as a reduced fraction.)

Explanation:

Step1: Cross - multiply the equation

To solve the rational equation \(\frac{-8}{7x}=\frac{1}{9x + 2}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\) (where \(b
eq0\) and \(d
eq0\)), then \(a\times d=b\times c\).
Applying this to our equation, we get \(-8\times(9x + 2)=7x\times1\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), where \(a=-8\), \(b = 9x\) and \(c = 2\), we have:
\(-8\times9x-8\times2=7x\)
\(-72x-16 = 7x\)

Step3: Move all \(x\) terms to one side

Add \(72x\) to both sides of the equation to get:
\(-16=7x + 72x\)

Step4: Combine like terms

Combine the \(x\) terms on the right - hand side: \(7x+72x = 79x\), so the equation becomes \(-16 = 79x\)

Step5: Solve for \(x\)

Divide both sides of the equation by \(79\) to isolate \(x\): \(x=\frac{-16}{79}\)

Answer:

\(\frac{-16}{79}\)