To solve the equation \( \frac{x + 7}{-2x} = \frac{5}{4} \), let's follow these steps:

### Step 1: Cross-multiply to eliminate the fractions
\[
4(x + 7) = 5(-2x)
\]
### Step 2: Expand both sides
\[
4x + 28 = -10x
\]

### Step 3: Move all terms involving \(x\) to one side
\[
4x + 10x = -28
\]
\[
14x = -28
\]

### Step 4: Solve for \(x\)
\[
x = \frac{-28}{14} = -2
\]

Thus, the solution is \( x = -2 \).

Would you like a detailed explanation or have any questions? Here are five related problems for practice:

1. Solve \( \frac{x - 3}{3x} = \frac{2}{5} \).
2. Solve \( \frac{2x + 4}{-x} = \frac{3}{2} \).
3. Solve \( \frac{3x - 5}{4x} = \frac{7}{6} \).
4. Solve \( \frac{x + 6}{5x} = \frac{8}{9} \).
5. Solve \( \frac{2x - 1}{-3x} = \frac{4}{5} \).

**Tip**: Always remember to check if cross-multiplying introduces any restrictions, like \(x = 0\) making the denominator zero!

Learn how to solve the linear equation x + 7 / -2x = 5 / 4 with a detailed step-by-step solution. This problem covers key algebraic concepts like cross-multiplication and equality of fractions theorem. Suitable for students in Grades 7-9.

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