Asked by BTS ARMY

Which of the following is an example of an equation with no solution?(1 point)
Responses

4x+3=3x+3
4 x plus 3 equals 3 x plus 3

3x+4=3x+3
3 x plus 4 equals 3 x plus 3

3x+4=3x+4
3 x plus 4 equals 3 x plus 4

3x+4=4x+3

Answers

Answered by BTS ARMY
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses

3x+4=3x+3
3 x plus 4 equals 3 x plus 3

3x+4=4x+3
3 x plus 4 equals 4 x plus 3

3x+4=3x+4
3 x plus 4 equals 3 x plus 4

4x+3=4x+3
Answered by BTS ARMY
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution.
The equation has no solution.

The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .

The equation has one solution: x=3.
Answered by BTS ARMY
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .

The equation has one solution: x=0.
Answered by BTS ARMY
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6(1 point)
Responses

The equation has no solution.
The equation has no solution.

The equation has one solution: x=10.
The equation has one solution: x equals 10 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=6.
Answered by GPT-4o mini
To determine which of the provided equations has no solution, let's analyze each option:

1. **4x + 3 = 3x + 3**
- Subtract 3x from both sides:
\( 4x - 3x + 3 = 3 \)
\( x + 3 = 3 \)
- Subtract 3 from both sides:
\( x = 0 \)
- **This equation has a solution** (x = 0).

2. **3x + 4 = 3x + 3**
- Subtract 3x from both sides:
\( 4 = 3 \)
- This statement is false; **there is no solution**.

3. **3x + 4 = 3x + 4**
- Subtract 3x + 4 from both sides:
\( 0 = 0 \)
- This statement is always true; **there are infinitely many solutions**.

4. **3x + 4 = 4x + 3**
- Subtract 3x from both sides:
\( 4 = x + 3 \)
- Subtract 3 from both sides:
\( x = 1 \)
- **This equation has a solution** (x = 1).

Thus, the equation with **no solution** is:

**3x + 4 = 3x + 3**.
Answered by GPT-4o mini
To find the equation with exactly one solution, we need to analyze each option:

1. **3x + 4 = 3x + 3**
- Subtract \(3x\) from both sides:
\[ 4 = 3 \]
- This statement is false; **there is no solution**.

2. **3x + 4 = 4x + 3**
- Subtract \(3x\) from both sides:
\[ 4 = x + 3 \]
- Subtract \(3\) from both sides:
\[ x = 1 \]
- **This equation has exactly one solution** (x = 1).

3. **3x + 4 = 3x + 4**
- Subtract \(3x + 4\) from both sides:
\[ 0 = 0 \]
- This statement is always true; **there are infinitely many solutions**.

4. **4x + 3 = 4x + 3**
- Similar to the previous one, subtract \(4x + 3\) from both sides:
\[ 0 = 0 \]
- Again, this statement is always true; **there are infinitely many solutions**.

Thus, the equation with **exactly one solution** is:

**3x + 4 = 4x + 3**.
Answered by GPT-4o mini
Let's solve the equation step by step:

Given:

\[ 3(x + 2) - 6 = 3x \]

1. Distribute on the left side:
\[ 3x + 6 - 6 = 3x \]

2. Simplify the left side:
\[ 3x = 3x \]

At this point, we can see that both sides of the equation are equal for any value of \( x \). This means that the equation is true for all values of \( x \).

Thus, the conclusion is:

**The equation has infinite solutions.**
Answered by GPT-4o mini
Let's solve the given equation step by step:

Given:

\[ 4x = 3(x + 5) - 15 \]

1. Distribute on the right side:
\[
4x = 3x + 15 - 15
\]
This simplifies to:
\[
4x = 3x + 0
\]

2. Now, subtract \(3x\) from both sides:
\[
4x - 3x = 0
\]
This simplifies to:
\[
x = 0
\]

Since we found one specific solution for \( x \):

**The equation has one solution: \( x = 0 \).**
Answered by GPT-4o mini
Let's solve the equation step by step:

Given:

\[ 5(2x + 2) - 7x = 3x + 6 \]

1. First, distribute \(5\) on the left side:
\[
10x + 10 - 7x = 3x + 6
\]

2. Combine like terms on the left side:
\[
(10x - 7x) + 10 = 3x + 6
\]
\[
3x + 10 = 3x + 6
\]

3. Now, subtract \(3x\) from both sides:
\[
10 = 6
\]

This statement is false, meaning there are no values of \(x\) that can satisfy this equation.

Thus, the conclusion is:

**The equation has no solution.**