Answer :

We start with the equation

$$
\frac{x}{7} + 10.1 = -1.1.
$$

**Step 1.** Subtract $10.1$ from both sides to isolate the term with $x$:

$$
\frac{x}{7} = -1.1 - 10.1 = -11.2.
$$

**Step 2.** Multiply both sides by $7$ to solve for $x$:

$$
x = -11.2 \times 7 \approx -78.4.
$$

Thus, the solution for $x$ is

$$
x = -78.4.
$$