Question

solve for x.
9(x + 1) = 25 + x
\\(\bigcirc\\) \\(x = 2\\)
\\(\bigcirc\\) \\(x = 3\\)
\\(\bigcirc\\) \\(x = 4\\)
\\(\bigcirc\\) \\(x = 5\\)

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(9(x + 1)\) to get \(9x+9\). So the equation becomes \(9x + 9=25 + x\).

Step2: Subtract \(x\) from both sides

Subtracting \(x\) from both sides gives \(9x - x+9=25 + x - x\), which simplifies to \(8x+9 = 25\).

Step3: Subtract 9 from both sides

Subtracting 9 from both sides: \(8x+9 - 9=25 - 9\), so \(8x=16\).

Step4: Divide both sides by 8

Dividing both sides by 8: \(\frac{8x}{8}=\frac{16}{8}\), which gives \(x = 2\).

Answer:

\(x = 2\) (corresponding to the option: \(x = 2\))