Solve the equation for x using algebraic methods. Show your work. 23x=4x+1 Note: Enter your answer and SHOW ALL THE STEPS NECESSARY to solve this problem in the space provided. You will not receive credit without all work shown. (You may use the image icon to upload your work)

Answer 1

To solve the equation \( 23x = 4x + 1 \), we will follow these algebraic steps:

1. Isolate the variable \( x \) by moving all terms involving \( x \) to one side of the equation. We start by subtracting \( 4x \) from both sides:

   \[ 23x - 4x = 4x + 1 - 4x \]

   Simplifying both sides gives:

   \[ 19x = 1 \]

2. Divide both sides by 19 to solve for \( x \):

   \[ x = \frac{1}{19} \]

Thus, the solution to the equation \( 23x = 4x + 1 \) is

\[ \boxed{\frac{1}{19}} \]

Verification: To ensure the solution is correct, substitute \( x = \frac{1}{19} \) back into the original equation:

• Left side:

  \[ 23\left(\frac{1}{19}\right) = \frac{23}{19} \]

• Right side:

  \[ 4\left(\frac{1}{19}\right) + 1 = \frac{4}{19} + 1 = \frac{4}{19} + \frac{19}{19} = \frac{23}{19} \]

Since both sides equal \( \frac{23}{19} \), our solution is verified.

The final answer remains:

\[ \boxed{\frac{1}{19}} \]