Solve for x in the equation −6.29(x+7.85)=−19.499.

Question

i got 4.75. am i correct?

Answer 1

Let's solve the equation step by step.

The equation is:

\[ -6.29(x + 7.85) = -19.499 \]

First, divide both sides by -6.29 to isolate the term in parentheses:

\[ x + 7.85 = \frac{-19.499}{-6.29} \]

Calculating the right-hand side:

\[ \frac{-19.499}{-6.29} \approx 3.1 \]

So now we have:

\[ x + 7.85 \approx 3.1 \]

Next, subtract 7.85 from both sides to solve for \(x\):

\[ x \approx 3.1 - 7.85 \]

Calculating this:

\[ x \approx 3.1 - 7.85 \approx -4.75 \]

Therefore, the correct solution for \(x\) is approximately \(-4.75\).

So, your answer of \(4.75\) is incorrect. The correct value is:

\[ x \approx -4.75 \]

Answer 2

in which steps??

Answer 3

Sure! Let's go through the steps to solve \(-6.29(x + 7.85) = -19.499\) in detail:

Step 1: Isolate the term in parentheses

Start by dividing both sides of the equation by \(-6.29\):

\[ x + 7.85 = \frac{-19.499}{-6.29} \]

Step 2: Simplify the right side

Now we calculate the right-hand side:

\[ \frac{-19.499}{-6.29} = \frac{19.499}{6.29} \]

Calculating that value gives approximately:

\[ \frac{19.499}{6.29} \approx 3.1 \]

So we update our equation to:

\[ x + 7.85 \approx 3.1 \]

Step 3: Solve for \(x\)

Next, subtract \(7.85\) from both sides to isolate \(x\):

\[ x \approx 3.1 - 7.85 \]

Step 4: Perform the subtraction

Now calculate \(3.1 - 7.85\):

\[ 3.1 - 7.85 = -4.75 \]

Conclusion

So the final answer is:

\[ x \approx -4.75 \]

Summary

1. Start with the equation: \(-6.29(x + 7.85) = -19.499\)
2. Divide by \(-6.29\) to isolate \(x + 7.85\).
3. Calculate \(\frac{19.499}{6.29} \approx 3.1\).
4. Set up the equation \(x + 7.85 \approx 3.1\).
5. Subtract \(7.85\) from both sides.
6. Get the final answer: \(x \approx -4.75\).

Your obtained answer of \(4.75\) was correct in magnitude (i.e., \(4.75\)), but the sign was incorrect; the solution should have been \(-4.75\).

Answer 4

no i mean in what step did i go wrong?

Answer 5

Let's identify where you might have gone wrong in your calculations. Here's a recap of the original problem and compare each step where you could have made an error.

Original Equation

\[ -6.29(x + 7.85) = -19.499 \]

Step 1: Divide by \(-6.29\)

You should divide both sides by \(-6.29\):

\[ x + 7.85 = \frac{-19.499}{-6.29} \]

• Possible Mistakes Here:
  • If you accidentally handled the division incorrectly or miscalculated, it could lead to an incorrect value for \(x + 7.85\).

Step 2: Calculating the Right Side

Calculating \(\frac{-19.499}{-6.29}\) leads to a positive number due to the double negatives. It should be:

\[ \frac{19.499}{6.29} \approx 3.1 \]

• Possible Mistakes Here:
  • If you did not recognize that the negatives cancel out and calculated incorrectly.

Step 3: Isolate \(x\)

The next step is:

\[ x + 7.85 \approx 3.1 \]

Step 4: Subtracting

Next, subtract \(7.85\) from both sides:

\[ x \approx 3.1 - 7.85 \]

• Where You Might Have Gone Wrong:
  • The mistake could have occurred in this subtraction step.

Final Calculation

Your final calculation:

\[ x \approx 3.1 - 7.85 \]

The correct result is:

\[ 3.1 - 7.85 = -4.75 \]

Summary of Possible Mistakes

1. Division: Miscalculating \(\frac{-19.499}{-6.29}\) and not realizing it should yield a positive result (should be around 3.1).

2. Subtraction: Incorrectly performing the subtraction \(3.1 - 7.85\), which should result in a negative value.

So, you likely miscalculated during the division step or in the subtraction, leading you to the incorrect result of \(4.75\) instead of \(-4.75\).

Answer 6

oh i got step 2 wrong
But why is the lowest number go first in the subtraction?

Answer 7

In subtraction, the order matters because it is not commutative, meaning \(a - b\) does not equal \(b - a\) in general. When you are subtracting, you are essentially determining how much more one number is compared to another.

Explanation of the Order in Subtraction

1. Understanding the Operation:

   • When you subtract \(b\) from \(a\), you are finding the difference between the two numbers: how many units you would need to add \(b\) back to reach \(a\).
   • For example: if \(a = 3.1\) and \(b = 7.85\), calculating \(3.1 - 7.85\) is asking, "How much less is \(3.1\) than \(7.85\)?"

2. Example:

   • If you think of it on a number line:
     • Point \(3.1\) is to the left of point \(7.85\).
     • Therefore, if you want to find how much shorter \(3.1\) is compared to \(7.85\), you'd end up with a negative number since you are moving left on the number line.
   • Thus, \(3.1 - 7.85 = -4.75\), indicating that \(3.1\) is \(4.75\) units less than \(7.85\).

3. Descending Order:

   • If you accidentally wrote \(7.85 - 3.1\), you'd be calculating how much more \(7.85\) is compared to \(3.1\), resulting in a positive number: \[ 7.85 - 3.1 = 4.75. \]

Conclusion

In arithmetic, the first number (the minuend) must be greater than or equal to the second number (the subtrahend) to avoid negative results in the context you are working with (if you're expecting a positive difference). For your equation:

• You correctly had \(3.1 - 7.85\), where \(3.1 < 7.85\), leading to a negative result of \(-4.75\).

This understanding of order is vital in ensuring accurate arithmetic operations.