Let's solve the equation step by step:

The equation is:

\[
\frac{4}{1} \cdot \left( x + \frac{5}{1} \right) = -\frac{10}{7}
\]

### Step 1: Simplify the terms.
- First, simplify the fractions:
\[
4(x + 5) = -\frac{10}{7}
\]

### Step 2: Distribute the \( 4 \) on the left-hand side.
\[
4x + 20 = -\frac{10}{7}
\]

### Step 3: Eliminate the constant on the left-hand side by subtracting \( 20 \) from both sides.
\[
4x = -\frac{10}{7} - 20
\]

### Step 4: Combine the terms on the right-hand side.
First, express \( 20 \) as a fraction with denominator 7:
\[
20 = \frac{140}{7}
\]

Now, subtract the fractions:
\[
-\frac{10}{7} - \frac{140}{7} = -\frac{150}{7}
\]

So, the equation becomes:
\[
4x = -\frac{150}{7}
\]

### Step 5: Solve for \( x \) by dividing both sides by \( 4 \):
\[
x = \frac{-150}{7 \times 4} = \frac{-150}{28}
\]

### Step 6: Simplify the fraction (if possible):
The greatest common divisor (GCD) of 150 and 28 is 2, so:
\[
x = \frac{-75}{14}
\]

Thus, the solution is:
\[
x = \frac{-75}{14}
\]

Would you like more details or further clarification?

### Related questions:
1. How do you simplify fractions involving negative numbers?
2. Can you solve equations involving mixed fractions?
3. How do you handle equations with multiple variables?
4. What are the steps to clear a fraction from an equation?
5. How do you check if a fraction in a solution is in its simplest form?

### Tip:
Always ensure your fractions are simplified by finding the greatest common divisor (GCD).

Learn how to solve the linear equation 4(x + 5) = −10/7 using algebraic methods. This problem involves simplifying fractions, distributing terms, and solving for x. Suitable for students in Grades 6-8.

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