Explore IDNLearn.com's extensive Q&A database and find the answers you need. Get step-by-step guidance for all your technical questions from our knowledgeable community members.
Sagot :
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
```
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
```
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.