Question

Rewrite the equation 4x3x−12+3=10
in two equations joined by “and.”

Answer 1

Can you answer it step by step

Answer 2

can you answer it simply, but also step by step

Answer 3

Thank you bot, you are one of the most helpful AI I have encountered

Answer 4

Demonstrate how to solve the equation 3.51.2x=5.4
for the variable x. Make sure to show each step.

Answer 5

Can you simplify the steps and make it more straightforward and broad?

Answer 6

You can rewrite the given equation \( 4x^3 - 12 + 3 = 10 \) as two equations joined by "and" as follows:

\( 4x^3 - 12 + 3 = 10 \) and \( 4x^3 - 12 + 3 - 10 = 0 \).

This simplifies to:

\( 4x^3 - 9 = 10 \) and \( 4x^3 - 9 = 0 \).

Answer 7

Certainly! Let's break down the process of rewriting the equation \( 4x^3 - 12 + 3 = 10 \) into two equations joined by "and" step by step.

### Step 1: Understand the Original Equation
The original equation is:
\[ 4x^3 - 12 + 3 = 10 \]

### Step 2: Simplify the Left Side
First, simplify the left side of the equation:
- Combine the constants \(-12\) and \(+3\):
\[
-12 + 3 = -9
\]
So the equation becomes:
\[ 4x^3 - 9 = 10 \]

### Step 3: Rearrange the Equation
Now, we can rearrange this equation to isolate one side:
\[ 4x^3 - 9 - 10 = 0 \]
This simplifies to:
\[ 4x^3 - 19 = 0 \]

### Step 4: Write Two Equations
We now have two forms:
1. The simplified version of the original equation:
\[
4x^3 - 9 = 10
\]
2. The arrangement set to zero:
\[
4x^3 - 19 = 0
\]

### Step 5: Combine with "and"
We can now write these as two equations joined by "and":
\[
4x^3 - 9 = 10 \quad \text{and} \quad 4x^3 - 19 = 0
\]

### Final Result
Thus, the original equation can be expressed as:
\[
4x^3 - 9 = 10 \quad \text{and} \quad 4x^3 - 19 = 0
\]

This concludes the step-by-step process!

Answer 8

Of course! Here's a simplified step-by-step breakdown of rewriting the equation \( 4x^3 - 12 + 3 = 10 \) into two equations joined by "and."

### Step 1: Start with the Original Equation
The original equation is:
\[
4x^3 - 12 + 3 = 10
\]

### Step 2: Simplify the Left Side
Combine the constants on the left side:
\[
-12 + 3 = -9
\]
So, we rewrite the equation as:
\[
4x^3 - 9 = 10
\]

### Step 3: Rearrange to Set One Side to Zero
Now, we manipulate the equation to set one side to zero:
\[
4x^3 - 9 - 10 = 0
\]
This simplifies to:
\[
4x^3 - 19 = 0
\]

### Step 4: Write Two Equations
Now we can write the two equations:
1. From the original format:
\[
4x^3 - 9 = 10
\]
2. From setting it to zero:
\[
4x^3 - 19 = 0
\]

### Step 5: Combine with "and"
We can now express these as:
\[
4x^3 - 9 = 10 \quad \text{and} \quad 4x^3 - 19 = 0
\]

### Final Result
The final answer is:
\[
4x^3 - 9 = 10 \quad \text{and} \quad 4x^3 - 19 = 0
\]

This completes the process!

Answer 9

Thank you so much for your kind words! I'm glad to hear that you found my assistance helpful. If you have any more questions or need further assistance, feel free to ask. I'm here to help!

Answer 10

Sure! Let's solve the equation \( 3.5 \cdot 1.2^x = 5.4 \) for the variable \( x \) step by step.

### Step 1: Isolate the Exponential Term
We start with the equation:
\[
3.5 \cdot 1.2^x = 5.4
\]
To isolate \( 1.2^x \), divide both sides of the equation by \( 3.5 \):
\[
1.2^x = \frac{5.4}{3.5}
\]

### Step 2: Calculate the Right Side
Now, calculate \( \frac{5.4}{3.5} \):
\[
\frac{5.4}{3.5} \approx 1.542857
\]
So we have:
\[
1.2^x \approx 1.542857
\]

### Step 3: Take the Logarithm of Both Sides
To solve for \( x \), take the logarithm (we can use natural logarithm \( \ln \) or common logarithm \( \log \)). Here we will use natural logarithm:
\[
\ln(1.2^x) = \ln(1.542857)
\]

### Step 4: Use the Power Rule of Logarithms
By applying the power rule of logarithms \( \ln(a^b) = b \cdot \ln(a) \), we get:
\[
x \cdot \ln(1.2) = \ln(1.542857)
\]

### Step 5: Solve for \( x \)
Now, divide both sides by \( \ln(1.2) \) to solve for \( x \):
\[
x = \frac{\ln(1.542857)}{\ln(1.2)}
\]

### Step 6: Calculate the Values
Now, use a calculator to find the values of the logarithms:
- \( \ln(1.542857) \approx 0.4343 \)
- \( \ln(1.2) \approx 0.1823 \)

Substituting these values into the equation:
\[
x \approx \frac{0.4343}{0.1823} \approx 2.384
\]

### Final Answer
Thus, the solution for \( x \) is approximately:
\[
x \approx 2.384
\]

If you need further assistance or clarification, feel free to ask!

Answer 11

Absolutely! Here’s a simplified and more straightforward approach to solving the equation \( 3.5 \cdot 1.2^x = 5.4 \):

### Step 1: Isolate the Exponential Term
- Start with the equation:
\[
3.5 \cdot 1.2^x = 5.4
\]
- Divide both sides by \( 3.5 \):
\[
1.2^x = \frac{5.4}{3.5}
\]

### Step 2: Simplify the Right Side
- Calculate \( \frac{5.4}{3.5} \):
\[
1.2^x = 1.542857 \quad (\text{approximately})
\]

### Step 3: Take the Logarithm
- Apply logarithm to both sides (we can use common logarithm \( \log \) or natural logarithm \( \ln \)):
\[
\log(1.2^x) = \log(1.542857)
\]

### Step 4: Use the Power Rule
- Using the power rule \( \log(a^b) = b \cdot \log(a) \):
\[
x \cdot \log(1.2) = \log(1.542857)
\]

### Step 5: Solve for \( x \)
- Rearrange to solve for \( x \):
\[
x = \frac{\log(1.542857)}{\log(1.2)}
\]

### Step 6: Calculate the Values
- Use a calculator to find the logarithmic values and compute \( x \):
- \( \log(1.542857) \approx 0.187 \)
- \( \log(1.2) \approx 0.079 \)

Using these values:
\[
x \approx \frac{0.187}{0.079} \approx 2.37 \quad (\text{approximately})
\]

### Final Answer
Thus, the solution is:
\[
x \approx 2.37
\]

This version condenses the steps while providing a clear direction for solving the equation! If you have any further questions, feel free to ask.