Question
Show how the equation would look after each step
5x−12−6x=−10x+7−1 (4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
5x−12−6x=−10x+7−1
Step 1: Combine like terms Response area,
Step 2: Get x-terms on same side of equation Response area
Step 3: Get constants on same side of equation Response area
Step 4: Get the x by itself by using the inverse operation
5x−12−6x=−10x+7−1 (4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
5x−12−6x=−10x+7−1
Step 1: Combine like terms Response area,
Step 2: Get x-terms on same side of equation Response area
Step 3: Get constants on same side of equation Response area
Step 4: Get the x by itself by using the inverse operation
Answers
GPT-4o mini
Sure! Here are the steps to solve the given equation \(5x - 12 - 6x = -10x + 7 - 1\) along with the results of each step.
**Step 1: Combine like terms**
- On the left side: \(5x - 6x = -x\)
- On the right side: \(7 - 1 = 6\)
So, the equation becomes:
\[
-x - 12 = -10x + 6
\]
---
**Step 2: Get x-terms on the same side of the equation**
- Add \(10x\) to both sides:
\[
-x + 10x - 12 = 6
\]
Which simplifies to:
\[
9x - 12 = 6
\]
---
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
Which simplifies to:
\[
9x = 18
\]
---
**Step 4: Get the x by itself by using the inverse operation**
- Divide by \(9\):
\[
x = \frac{18}{9}
\]
Which simplifies to:
\[
x = 2
\]
So the final answer is \(x = 2\).
**Step 1: Combine like terms**
- On the left side: \(5x - 6x = -x\)
- On the right side: \(7 - 1 = 6\)
So, the equation becomes:
\[
-x - 12 = -10x + 6
\]
---
**Step 2: Get x-terms on the same side of the equation**
- Add \(10x\) to both sides:
\[
-x + 10x - 12 = 6
\]
Which simplifies to:
\[
9x - 12 = 6
\]
---
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
Which simplifies to:
\[
9x = 18
\]
---
**Step 4: Get the x by itself by using the inverse operation**
- Divide by \(9\):
\[
x = \frac{18}{9}
\]
Which simplifies to:
\[
x = 2
\]
So the final answer is \(x = 2\).
try again for step 3
GPT-4o mini
Sure! Let's re-evaluate Step 3 of the equation. Here's the problem again for reference:
Starting from the result after Step 2:
\[
9x - 12 = 6
\]
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]
So, Step 3 correctly results in:
\[
9x = 18
\]
If the intent was to consider moving constants differently, we could also explore that, but the above approach is the typical way to isolate the x-term. Please let me know if there's a specific method or adjustment you want!
Starting from the result after Step 2:
\[
9x - 12 = 6
\]
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]
So, Step 3 correctly results in:
\[
9x = 18
\]
If the intent was to consider moving constants differently, we could also explore that, but the above approach is the typical way to isolate the x-term. Please let me know if there's a specific method or adjustment you want!
the options are:
1. 5 - 18x = -3x - 1
2. 1x - 12 = -10x + 6
3. -12 = -11x + 6
4. -12 = -9x + 6
5. -18 = 9x
6. -6 = -9x
7. -18 = -9x
1. 5 - 18x = -3x - 1
2. 1x - 12 = -10x + 6
3. -12 = -11x + 6
4. -12 = -9x + 6
5. -18 = 9x
6. -6 = -9x
7. -18 = -9x
GPT-4o mini
Thank you for providing the options! Let's go through the steps again to properly identify Step 3 with respect to the options you've given.
Starting from Step 2:
\[
9x - 12 = 6
\]
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]
Now, if we move the constants to the other side differently, we could rewrite it as:
\[
-12 = 18 - 9x
\]
To isolate the terms differently, we can subtract \(6\) from \(18\):
Bringing constants to one side of the equation, it can be expressed as:
\[
-12 = -9x + 6
\]
So, the correct option for Step 3 is:
**3. -12 = -9x + 6**
This confirms that when we rearrange the equation accordingly, we see the constants effectively positioned on one side and the terms involving \(x\) on the other.
Let’s summarize the adjusted steps:
1. Initial equation: \(5x - 12 - 6x = -10x + 7 - 1\)
2. Combine like terms: \(-x - 12 = -10x + 6\)
3. Get \(x\)-terms on the same side: \(9x - 12 = 6\)
4. Constants moved: **-12 = -9x + 6** (as per option 3).
Then,
5. Move \(6\) to the left to isolate \(x\) terms, resulting in: \(-12 - 6 = -9x\) leading to **-18 = -9x** (which is option 7).
If you have any further adjustments, feel free to mention them!
Starting from Step 2:
\[
9x - 12 = 6
\]
**Step 3: Get constants on the same side of the equation**
- Add \(12\) to both sides:
\[
9x - 12 + 12 = 6 + 12
\]
This simplifies to:
\[
9x = 18
\]
Now, if we move the constants to the other side differently, we could rewrite it as:
\[
-12 = 18 - 9x
\]
To isolate the terms differently, we can subtract \(6\) from \(18\):
Bringing constants to one side of the equation, it can be expressed as:
\[
-12 = -9x + 6
\]
So, the correct option for Step 3 is:
**3. -12 = -9x + 6**
This confirms that when we rearrange the equation accordingly, we see the constants effectively positioned on one side and the terms involving \(x\) on the other.
Let’s summarize the adjusted steps:
1. Initial equation: \(5x - 12 - 6x = -10x + 7 - 1\)
2. Combine like terms: \(-x - 12 = -10x + 6\)
3. Get \(x\)-terms on the same side: \(9x - 12 = 6\)
4. Constants moved: **-12 = -9x + 6** (as per option 3).
Then,
5. Move \(6\) to the left to isolate \(x\) terms, resulting in: \(-12 - 6 = -9x\) leading to **-18 = -9x** (which is option 7).
If you have any further adjustments, feel free to mention them!