Let's solve the equation:

\[
\frac{1}{4}x + \frac{1}{10} = -\frac{3}{20}x - \frac{7}{10}
\]

### Step 1: Eliminate fractions by finding the least common denominator (LCD).
The denominators are 4, 10, 20, and 10. The LCD of these numbers is 20. Multiply the entire equation by 20 to eliminate the fractions:

\[
20 \times \left(\frac{1}{4}x\right) + 20 \times \left(\frac{1}{10}\right) = 20 \times \left(-\frac{3}{20}x\right) + 20 \times \left(-\frac{7}{10}\right)
\]

This simplifies to:

\[
5x + 2 = -3x - 14
\]

### Step 2: Combine like terms.
Move the \(x\)-terms to one side and the constant terms to the other side. Add \(3x\) to both sides:

\[
5x + 3x + 2 = -14
\]

Simplifying:

\[
8x + 2 = -14
\]

### Step 3: Solve for \(x\).
Subtract 2 from both sides:

\[
8x = -16
\]

Now, divide both sides by 8:

\[
x = -2
\]

### Final Answer:
\[
x = -2
\]

Do you want details on any step, or do you have any questions?

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Here are 5 related questions for further practice:

1. Solve: \(\frac{3}{5}x + \frac{1}{4} = \frac{2}{3}x - \frac{5}{6}\)
2. Solve: \(\frac{2}{7}x + \frac{5}{14} = \frac{3}{7}x - \frac{1}{2}\)
3. Solve: \(3x + 5 = 2x - 7\)
4. Solve: \(\frac{x}{6} + \frac{1}{8} = \frac{3x}{4} - \frac{5}{8}\)
5. Solve: \(2x - \frac{1}{3} = \frac{4}{5}x + \frac{7}{15}\)

**Tip:** When dealing with fractions in equations, multiplying through by the least common denominator simplifies the process.

Learn how to solve the linear equation 1/4x + 1/10 = -3/20x - 7/10 with a step-by-step guide. This problem covers algebraic concepts such as combining like terms and eliminating fractions using the least common denominator (LCD). Suitable for Grades 7-9 students.

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