Question

question
solve for x and simplify the answer fully.
\\(\frac{4x - 8}{2} = \frac{3x - 9}{3}\\)

Explanation:

Step1: Cross - multiply to eliminate denominators

To solve the equation \(\frac{4x - 8}{2}=\frac{3x - 9}{3}\), we can cross - multiply. Cross - multiplying gives us \(3(4x - 8)=2(3x - 9)\).

Step2: Expand both sides

Expanding the left - hand side: \(3\times4x-3\times8 = 12x-24\).
Expanding the right - hand side: \(2\times3x-2\times9=6x - 18\).
So our equation becomes \(12x-24 = 6x-18\).

Step3: Subtract \(6x\) from both sides

Subtracting \(6x\) from both sides of the equation \(12x-24 = 6x-18\) gives: \(12x-6x-24=6x - 6x-18\), which simplifies to \(6x-24=-18\).

Step4: Add 24 to both sides

Adding 24 to both sides of the equation \(6x-24=-18\) gives: \(6x-24 + 24=-18 + 24\), so \(6x=6\).

Step5: Divide both sides by 6

Dividing both sides of the equation \(6x = 6\) by 6 gives: \(x=\frac{6}{6}=1\).

Answer:

\(x = 1\)