A number divided by nine, minus five times the number, is equal to one more than the number.

Let's translate the problem into an algebraic equation.

Let the unknown number be \( x \).

According to the problem:
- "A number divided by nine" is \( \frac{x}{9} \).
- "Minus five times the number" is \( -5x \).
- "Is equal to one more than the number" is \( = x + 1 \).

So the equation is:

\[
\frac{x}{9} - 5x = x + 1
\]

Now, let's solve this equation step by step.

### Step 1: Eliminate the fraction
Multiply every term by 9 to get rid of the fraction:

\[
x - 45x = 9x + 9
\]

### Step 2: Combine like terms
Simplify the equation:

\[
-44x = 9x + 9
\]

### Step 3: Move all terms involving \( x \) to one side
Subtract \( 9x \) from both sides:

\[
-53x = 9
\]

### Step 4: Solve for \( x \)
Divide both sides by \( -53 \):

\[
x = -\frac{9}{53}
\]

So, the solution is:

\[
x = -\frac{9}{53}
\]

### Final Answer:
The number is \( x = -\frac{9}{53} \).

Would you like more details or have any other questions?

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Learn how to solve the equation: A number divided by nine, minus five times the number, equals one more than the number. This problem involves algebraic equations and fractions, suitable for students in Grades 7-9.

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