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

Subtract \(x\) from each side of the equation: \(9x - x+9=25 + x - x\), which simplifies to \(8x+9 = 25\).

Step3: Subtract 9 from both sides

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

Step4: Divide by 8

Divide both sides by 8: \(\frac{8x}{8}=\frac{16}{8}\), which gives \(x = 2\). Wait, no, wait, let's check again. Wait, \(25-9 = 16\), \(8x=16\), \(x = 2\)? Wait, no, wait, let's re - solve:

Wait, original equation \(9(x + 1)=25 + x\)

Expand left side: \(9x+9=25 + x\)

Subtract \(x\) from both sides: \(9x - x+9=25+x - x\) → \(8x + 9=25\)

Subtract 9: \(8x=25 - 9=16\)

Divide by 8: \(x=\frac{16}{8}=2\)? Wait, but let's check by plugging \(x = 2\) into the original equation:

Left side: \(9(2 + 1)=9\times3 = 27\)

Right side: \(25+2=27\). Oh, right, so \(x = 2\) is correct. Wait, but earlier when I thought I made a mistake, but it's correct.

Wait, but let's check the options. The first option is \(x = 2\).

Wait, but let's do the solving again carefully:

\(9(x + 1)=25 + x\)

1. Distribute 9: \(9x+9 = 25+x\)
2. Subtract \(x\) from both sides: \(9x - x+9=25+x - x\) → \(8x + 9=25\)
3. Subtract 9: \(8x=25 - 9=16\)
4. Divide by 8: \(x = 2\)

Answer:

A. \(x = 2\)