$$  $$$\frac{2\left(7+x\right)}{-2}=\frac{-5}{-2}$

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

### Step 1: Simplify both sides of the equation.
First, simplify the left side of the equation:

\[
\frac{2(7+x)}{-2} = \frac{2 \cdot (7+x)}{-2} = \frac{2 \cdot 7 + 2 \cdot x}{-2} = \frac{14 + 2x}{-2} 
\]

Simplifying the expression:

\[
\frac{14 + 2x}{-2} = \frac{14}{-2} + \frac{2x}{-2} = -7 - x
\]

Next, simplify the right side:

\[
\frac{-5}{-2} = \frac{-5}{-2} = \frac{5}{2}
\]

### Step 2: Set up the simplified equation.
Now we have:

\[
-7 - x = \frac{5}{2}
\]

### Step 3: Solve for $x$.
To isolate $x$, add $7$ to both sides:

\[
-x = \frac{5}{2} + 7
\]

Convert $7$ to a fraction with a denominator of 2:

\[
7 = \frac{14}{2}
\]

So,

\[
-x = \frac{5}{2} + \frac{14}{2} = \frac{19}{2}
\]

Finally, multiply both sides by $-1$ to solve for $x$:

\[
x = -\frac{19}{2}
\]

### Final Answer:
\[
x = -\frac{19}{2}
\]

This is the solution for $x$.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How can this method be applied to other linear equations?
2. What happens if the equation involves more complex fractions?
3. How does multiplying both sides by the same number affect an equation?
4. What are some real-world applications of solving linear equations?
5. How can you check if your solution to an equation is correct?

**Tip:** Always simplify both sides of the equation as much as possible before solving for the variable. This can make the solving process much easier.

$\frac{2\left(7+x\right)}{-2}=\frac{-5}{-2}$

Learn how to solve the linear equation $\frac{2(7+x)}{-2} = \frac{-5}{-2}$ through a step-by-step process. This solution covers key algebraic concepts such as simplifying fractions and isolating variables. Ideal for students in Grades 7-8.

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