Question

solve for x and simplify the answer fully.\\(\frac{x + 9}{5} = \frac{x + 3}{8}\\)\
answer attempt 1 out of 2\
\\(x = \\) input box submit answer

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{x + 9}{5}=\frac{x + 3}{8}\), we cross - multiply. Cross - multiplying gives us \(8(x + 9)=5(x + 3)\).

Step2: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side: \(8x+72\) and the right - hand side: \(5x + 15\). So the equation becomes \(8x+72 = 5x+15\).

Step3: Subtract \(5x\) from both sides

Subtracting \(5x\) from both sides of the equation \(8x+72 = 5x+15\) gives \(8x-5x+72=5x - 5x+15\), which simplifies to \(3x+72 = 15\).

Step4: Subtract 72 from both sides

Subtracting 72 from both sides of the equation \(3x+72 = 15\) gives \(3x+72-72=15 - 72\), which simplifies to \(3x=-57\).

Step5: Divide both sides by 3

Dividing both sides of the equation \(3x=-57\) by 3 gives \(x=\frac{-57}{3}=-19\).

Answer:

\(x=-19\)