Asked by AYD3N

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

• 3x + 4 = 4x + 3

• 4x + 3 = 3x + 3

03x + 4 = 3x + 4

03x +4=3x+3
Answered by AYD3N
Which of the following is an example of an equation with exactly one solution? (1 point)

03x+4= 3x+3

• 3x+4 = 3x+4

03x+4=4x+3

04x +3=4x+3
Answered by AYD3N
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2) - 6 = 3x (1 point)

• The equation has no solution.

• The equation has one solution: x = -3.

• The equation has one solution: x = 3.

• The equation has infinite solutions.
Answered by AYD3N
Solve for x to determine if the equation has one, none, or infinite solutions.
4х =3 x+5) - 15 (1 point)
• The equation has no solution.
• The equation has one solution: 2 = 0.
• The equation has one solution: x = - 10.
• The equation has infinite solutions.
Answered by AYD3N
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x + 2) - 7x=3x + 6 (1 point)

• The equation has one solution: x = 6.

• The equation has infinite solutions.

• The equation has one solution: x = 10.

• The equation has no solution.
Answered by GPT-4o mini
To determine which equation has no solution, we can solve each one:

1. **3x + 4 = 4x + 3**
- Rearranging gives: \(3x - 4x = 3 - 4\)
- This simplifies to: \(-x = -1\)
- Therefore, \(x = 1\). (This has a solution)

2. **4x + 3 = 3x + 3**
- Rearranging gives: \(4x - 3x = 3 - 3\)
- This simplifies to: \(x = 0\). (This has a solution)

3. **3x + 4 = 3x + 4**
- This equality holds for all values of \(x\), so it has infinitely many solutions (not applicable here as having no solution).

4. **3x + 4 = 3x + 3**
- Rearranging gives: \(3x - 3x = 3 - 4\)
- This simplifies to: \(0 = -1\), which is a contradiction. (This has no solution)

The equation with no solution is: **3x + 4 = 3x + 3**.
Answered by GPT-4o mini
To find the equation with exactly one solution, we can analyze each option:

1. **3x + 4 = 3x + 3**
- Rearranging gives: \(3x - 3x = 3 - 4\)
- This simplifies to: \(0 = -1\), which is a contradiction. (This has no solution.)

2. **3x + 4 = 3x + 4**
- This equality holds true for all values of \(x\), so it has infinitely many solutions. (Not applicable here.)

3. **3x + 4 = 4x + 3**
- Rearranging gives: \(3x - 4x = 3 - 4\)
- This simplifies to: \(-x = -1\)
- Therefore, \(x = 1\). (This has exactly one solution.)

4. **4x + 3 = 4x + 3**
- This equality also holds true for all values of \(x\), so it has infinitely many solutions. (Not applicable here.)

The equation with exactly one solution is: **3x + 4 = 4x + 3**.
Answered by GPT-4o mini
Let's solve the given equation step by step:

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

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

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

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

Thus, the equation has **infinite solutions**.

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

Given:
\[ 4x = 3x + 5 - 15 \]

1. Simplify the right side:
\[ 4x = 3x + 5 - 15 \]
\[ 4x = 3x - 10 \]

2. Subtract \(3x\) from both sides:
\[ 4x - 3x = -10 \]
\[ x = -10 \]

Now we've found that the equation has **one solution: \(x = -10\)**.

So the correct answer is: **The equation has one solution: x = -10.**
Answered by GPT-4o mini
Let's solve the equation step by step:

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

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

At this point, we see that \(10 = 6\) is a false statement. This indicates that there is no value for \(x\) that can satisfy the equation.

Thus, the equation has **no solution**.

So the correct answer is: **The equation has no solution.**