Question

practice: solve rational equations
score: 2/6 answered: 2/6
question 3
solve the equation
\\(\frac{6}{4x} = \frac{-7}{4x + 2}\\)
\\(x = \square\\) (if needed, enter your answer as a reduced fraction.)

Explanation:

Step1: Cross - multiply the equation

To solve the rational equation \(\frac{6}{4x}=\frac{-7}{4x + 2}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So we have \(6\times(4x + 2)=-7\times(4x)\).

Step2: Expand both sides

Expand the left - hand side: \(6\times4x+6\times2 = 24x+12\).
Expand the right - hand side: \(-7\times4x=-28x\).
So the equation becomes \(24x + 12=-28x\).

Step3: Add \(28x\) to both sides

Add \(28x\) to each side of the equation \(24x + 12=-28x\) to get \(24x+28x + 12=-28x+28x\).
Simplifying, we have \(52x+12 = 0\).

Step4: Subtract 12 from both sides

Subtract 12 from both sides of the equation \(52x+12 = 0\): \(52x+12-12=0 - 12\).
Simplifying, we get \(52x=-12\).

Step5: Solve for \(x\)

Divide both sides of the equation \(52x=-12\) by 52: \(x=\frac{-12}{52}\).
Reduce the fraction \(\frac{-12}{52}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So \(x=\frac{-12\div4}{52\div4}=\frac{-3}{13}\).

Answer:

\(x =-\frac{3}{13}\)