Question

solve for x and simplify the answer fully:
\\(\frac{6}{x - 3} = \frac{3}{2x + 1}\\)
answer attempt 1 out of 4
x =

Explanation:

Step1: Cross - multiply the fractions

Given the equation \(\frac{6}{x - 3}=\frac{3}{2x+1}\), cross - multiplying (which is valid when \(x
eq3\) and \(x
eq-\frac{1}{2}\) to avoid division by zero) gives us \(6(2x + 1)=3(x - 3)\).

Step2: Expand both sides

Expand the left - hand side: \(6\times2x+6\times1 = 12x + 6\).
Expand the right - hand side: \(3\times x-3\times3=3x - 9\).
So the equation becomes \(12x + 6=3x - 9\).

Step3: Subtract \(3x\) from both sides

Subtract \(3x\) from each side: \(12x-3x + 6=3x-3x - 9\), which simplifies to \(9x+6=-9\).

Step4: Subtract 6 from both sides

Subtract 6 from each side: \(9x+6 - 6=-9 - 6\), so \(9x=-15\).

Step5: Divide both sides by 9

Divide both sides by 9: \(x=\frac{-15}{9}\).

Step6: Simplify the fraction

Simplify \(\frac{-15}{9}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(x =-\frac{5}{3}\).

Answer:

\(x =-\frac{5}{3}\)