We are tasked with solving the equation:

\[
\frac{290 - x}{1.25} = 40
\]

### Step 1: Eliminate the denominator
Multiply both sides of the equation by 1.25 to eliminate the fraction:

\[
290 - x = 40 \times 1.25
\]

### Step 2: Simplify the right-hand side
\[
40 \times 1.25 = 50
\]

Now the equation becomes:
\[
290 - x = 50
\]

### Step 3: Solve for \(x\)
Subtract 290 from both sides to isolate \(x\):

\[
-x = 50 - 290
\]

\[
-x = -240
\]

### Step 4: Simplify
Multiply both sides by -1 to get \(x\):

\[
x = 240
\]

Thus, the solution is:

\[
x = 240
\]

Would you like more details or clarifications on any step?

Here are 5 related questions:
1. What happens if you multiply both sides of the equation by 2.5 instead of 1.25?
2. How would you solve this equation: \(\frac{400 - x}{2.5} = 100\)?
3. What is the value of \(x\) if the equation was \(\frac{290 - x}{1.25} = 30\)?
4. Can you solve \(290 - x = 1.25 \times 50\)?
5. How would this equation change if the right side was 45 instead of 40?

**Tip**: Always ensure to clear any fractions in an equation first by multiplying both sides by the denominator, which simplifies the solving process.

Learn how to solve the linear equation 290 - x / 1.25 = 40 with a step-by-step solution. This problem covers core algebraic concepts, including fraction elimination and basic equation solving techniques. Suitable for students in Grades 7-9.

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