Question
Complete the following tasks for this equation:
b/7.8=-2.15
Give an estimate for the solution. Be sure to explain how you arrived at the estimate, either by showing an equation or in words.
Solve the equation. Show or explain your work.
Compared to your estimate, is your answer reasonable? Explain your answer in complete sentences.
b/7.8=-2.15
Give an estimate for the solution. Be sure to explain how you arrived at the estimate, either by showing an equation or in words.
Solve the equation. Show or explain your work.
Compared to your estimate, is your answer reasonable? Explain your answer in complete sentences.
Answers
Answer
can you make it less advanced
Answer
can you use lees words and mae it just a little less advanced
Answered by
GPT-4o mini
### Step 1: Estimate the Solution
The equation given is
\[
\frac{b}{7.8} = -2.15
\]
To estimate the value of \(b\), we can multiply both sides by 8 (a close estimation of 7.8) to simplify our calculations. Thus, we have:
\[
b \approx -2.15 \times 8
\]
Calculating this gives:
\[
-2.15 \times 8 = -17.2
\]
So, our estimate for \(b\) is approximately \(-17.2\).
### Step 2: Solve the Equation
Now, let’s solve the equation exactly. We start from the original equation:
\[
\frac{b}{7.8} = -2.15
\]
To isolate \(b\), we can multiply both sides by 7.8:
\[
b = -2.15 \times 7.8
\]
Now let’s perform the multiplication:
\[
b = -16.83
\]
### Step 3: Comparison of Estimate and Actual Answer
Our estimate for \(b\) was \(-17.2\) and we found the exact solution to be \(-16.83\).
Comparing the two:
- **Estimate**: \(-17.2\)
- **Exact Solution**: \(-16.83\)
The exact solution of \(-16.83\) is quite close to the estimate of \(-17.2\), indicating that our estimation method was effective.
### Conclusion
In conclusion, my estimation was reasonably close to the actual solution of the equation. The estimate of \(-17.2\) gave a good approximation, as \(-16.83\) is only slightly higher than \(-17.2\). This demonstrates that using a rounded number for calculations can provide a useful initial insight into the solution.
The equation given is
\[
\frac{b}{7.8} = -2.15
\]
To estimate the value of \(b\), we can multiply both sides by 8 (a close estimation of 7.8) to simplify our calculations. Thus, we have:
\[
b \approx -2.15 \times 8
\]
Calculating this gives:
\[
-2.15 \times 8 = -17.2
\]
So, our estimate for \(b\) is approximately \(-17.2\).
### Step 2: Solve the Equation
Now, let’s solve the equation exactly. We start from the original equation:
\[
\frac{b}{7.8} = -2.15
\]
To isolate \(b\), we can multiply both sides by 7.8:
\[
b = -2.15 \times 7.8
\]
Now let’s perform the multiplication:
\[
b = -16.83
\]
### Step 3: Comparison of Estimate and Actual Answer
Our estimate for \(b\) was \(-17.2\) and we found the exact solution to be \(-16.83\).
Comparing the two:
- **Estimate**: \(-17.2\)
- **Exact Solution**: \(-16.83\)
The exact solution of \(-16.83\) is quite close to the estimate of \(-17.2\), indicating that our estimation method was effective.
### Conclusion
In conclusion, my estimation was reasonably close to the actual solution of the equation. The estimate of \(-17.2\) gave a good approximation, as \(-16.83\) is only slightly higher than \(-17.2\). This demonstrates that using a rounded number for calculations can provide a useful initial insight into the solution.
Answered by
GPT-4o mini
Sure! Let's break it down into simpler steps.
### Step 1: Estimate the Solution
The equation we have is:
\[
\frac{b}{7.8} = -2.15
\]
To estimate \(b\), we can round \(7.8\) to \(8\), which is easier to work with. So, we can think about it like this:
We want to find out what \(b\) would be if \(b\) divided by \(8\) equals \(-2.15\).
So, we can write:
\[
b \approx -2.15 \times 8
\]
Now let's do the multiplication:
\[
-2.15 \times 8 = -17.2
\]
Thus, our estimate for \(b\) is about \(-17.2\).
### Step 2: Solve the Equation
Now, let’s solve the equation exactly. We start from:
\[
\frac{b}{7.8} = -2.15
\]
To solve for \(b\), we can multiply both sides by \(7.8\). This helps us get \(b\) by itself. It looks like this:
\[
b = -2.15 \times 7.8
\]
Now we calculate that:
\[
-2.15 \times 7.8 \approx -16.83
\]
So the exact solution is \(b = -16.83\).
### Step 3: Compare Estimate and Exact Answer
We estimated that \(b\) is about \(-17.2\) and found out that the exact answer is \(-16.83\).
- **Estimate**: \(-17.2\)
- **Exact Answer**: \(-16.83\)
The exact answer, \(-16.83\), is very close to our estimate of \(-17.2\). This means our estimation method worked pretty well!
### Conclusion
In summary, our estimate of \(-17.2\) was a good guess because it is close to the actual solution of \(-16.83\). This shows that sometimes rounding numbers can help make calculations easier and still provide a reasonable answer!
### Step 1: Estimate the Solution
The equation we have is:
\[
\frac{b}{7.8} = -2.15
\]
To estimate \(b\), we can round \(7.8\) to \(8\), which is easier to work with. So, we can think about it like this:
We want to find out what \(b\) would be if \(b\) divided by \(8\) equals \(-2.15\).
So, we can write:
\[
b \approx -2.15 \times 8
\]
Now let's do the multiplication:
\[
-2.15 \times 8 = -17.2
\]
Thus, our estimate for \(b\) is about \(-17.2\).
### Step 2: Solve the Equation
Now, let’s solve the equation exactly. We start from:
\[
\frac{b}{7.8} = -2.15
\]
To solve for \(b\), we can multiply both sides by \(7.8\). This helps us get \(b\) by itself. It looks like this:
\[
b = -2.15 \times 7.8
\]
Now we calculate that:
\[
-2.15 \times 7.8 \approx -16.83
\]
So the exact solution is \(b = -16.83\).
### Step 3: Compare Estimate and Exact Answer
We estimated that \(b\) is about \(-17.2\) and found out that the exact answer is \(-16.83\).
- **Estimate**: \(-17.2\)
- **Exact Answer**: \(-16.83\)
The exact answer, \(-16.83\), is very close to our estimate of \(-17.2\). This means our estimation method worked pretty well!
### Conclusion
In summary, our estimate of \(-17.2\) was a good guess because it is close to the actual solution of \(-16.83\). This shows that sometimes rounding numbers can help make calculations easier and still provide a reasonable answer!
Answered by
GPT-4o mini
Of course! Here’s a simpler version with fewer words:
### Step 1: Estimate the Solution
We have the equation:
\[
\frac{b}{7.8} = -2.15
\]
To estimate \(b\), round \(7.8\) to \(8\). So, we multiply:
\[
b \approx -2.15 \times 8 = -17.2
\]
### Step 2: Solve the Equation
Now, let’s find the exact answer. From the original equation:
\[
\frac{b}{7.8} = -2.15
\]
Multiply both sides by \(7.8\):
\[
b = -2.15 \times 7.8
\]
Calculating gives:
\[
b = -16.83
\]
### Step 3: Compare Estimate and Exact Answer
- **Estimate**: \(-17.2\)
- **Exact Answer**: \(-16.83\)
The exact answer \(-16.83\) is close to the estimate \(-17.2\).
### Conclusion
Our estimate was pretty good! It shows that rounding can help us get a useful answer.
### Step 1: Estimate the Solution
We have the equation:
\[
\frac{b}{7.8} = -2.15
\]
To estimate \(b\), round \(7.8\) to \(8\). So, we multiply:
\[
b \approx -2.15 \times 8 = -17.2
\]
### Step 2: Solve the Equation
Now, let’s find the exact answer. From the original equation:
\[
\frac{b}{7.8} = -2.15
\]
Multiply both sides by \(7.8\):
\[
b = -2.15 \times 7.8
\]
Calculating gives:
\[
b = -16.83
\]
### Step 3: Compare Estimate and Exact Answer
- **Estimate**: \(-17.2\)
- **Exact Answer**: \(-16.83\)
The exact answer \(-16.83\) is close to the estimate \(-17.2\).
### Conclusion
Our estimate was pretty good! It shows that rounding can help us get a useful answer.
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