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The equation given is:

\[
-\frac{2}{5}x - \frac{7}{20}x + \frac{1}{4}x = -30
\]

Let's solve for \( x \):

### Step 1: Find a common denominator
The denominators involved are 5, 20, and 4. The least common denominator (LCD) is 20. Rewriting all fractions with a denominator of 20:

\[
-\frac{2}{5}x = -\frac{8}{20}x, \quad \frac{1}{4}x = \frac{5}{20}x
\]

So, the equation becomes:

\[
-\frac{8}{20}x - \frac{7}{20}x + \frac{5}{20}x = -30
\]

### Step 2: Combine like terms
Now combine the terms on the left-hand side:

\[
\left(-\frac{8}{20} - \frac{7}{20} + \frac{5}{20}\right)x = -30
\]

\[
\frac{-8 - 7 + 5}{20}x = -30
\]

\[
\frac{-10}{20}x = -30
\]

\[
-\frac{1}{2}x = -30
\]

### Step 3: Solve for \( x \)
Multiply both sides by \(-2\) to eliminate the fraction:

\[
x = -30 \times -2
\]

\[
x = 60
\]

Thus, the solution is:

\[
x = 60
\]

Would you like more details on any of the steps or have any further questions?

Here are 5 related questions to explore:

1. How do you find the least common denominator for fractions?
2. What are some common techniques for solving linear equations with fractions?
3. How can we check the solution by substituting the value of \( x \) back into the original equation?
4. What happens if one of the coefficients in the equation is zero?
5. How would the solution process differ if one side of the equation had fractions with variables and the other side had a whole number?

**Tip:** Always simplify fractions early in the process to make solving equations with multiple fractions easier.

Solve for x: - (2/5)x - (7/20)x + (1/4)x = -30

Learn how to solve a linear equation with fractions, specifically - (2/5)x - (7/20)x + (1/4)x = -30. This step-by-step guide walks through finding the least common denominator, simplifying the equation, and solving for x. Ideal for students in Grades 7-9.

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