Question

solve for x and simplify the answer fully.\\(\frac{x - 3}{5} = \frac{4x - 4}{6}\\)\
answer attempt 1 out of 2\
x =

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{x - 3}{5}=\frac{4x - 4}{6}\), we cross - multiply. Cross - multiplying gives us \(6(x - 3)=5(4x - 4)\).

Step2: Expand both sides

Expand the left - hand side: \(6\times x-6\times3 = 6x-18\).
Expand the right - hand side: \(5\times4x-5\times4=20x - 20\).
So the equation becomes \(6x-18 = 20x-20\).

Step3: Move the x - terms to one side and constants to the other

Subtract \(6x\) from both sides: \(6x-18-6x=20x - 20-6x\), which simplifies to \(-18 = 14x-20\).
Then add 20 to both sides: \(-18 + 20=14x-20 + 20\), so \(2 = 14x\).

Step4: Solve for x

Divide both sides by 14: \(x=\frac{2}{14}\). Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2. So \(x=\frac{1}{7}\).

Answer:

\(x = \frac{1}{7}\)