To solve the equation [tex]\(-\frac{1}{5}(x-25) = 7\)[/tex], it is essential to understand the correct sequence of operations to isolate [tex]\(x\)[/tex]. Here’s a step-by-step breakdown:
1. Identify the equation:
[tex]\[
-\frac{1}{5}(x-25) = 7
\][/tex]
2. Multiply each side by -5:
The first operation is to eliminate the fraction by multiplying both sides of the equation by -5. This helps to isolate the term with [tex]\(x\)[/tex].
[tex]\[
-5 \cdot \left( -\frac{1}{5}(x-25) \right) = -5 \cdot 7
\][/tex]
Simplify the left side:
[tex]\[
(x - 25) = -35
\][/tex]
3. Add 25 to both sides:
Now, to isolate [tex]\(x\)[/tex], add 25 to both sides of the equation.
[tex]\[
x - 25 + 25 = -35 + 25
\][/tex]
Simplify:
[tex]\[
x = -10
\][/tex]
Therefore, the correct sequence of operations to solve the equation is:
- Multiply each side by -5
- Add 25 to each side
Thus, the correct answer is:
```
Multiply each side by -5 , add 25 to each side
```
