Asked by Just-A-V3nter

Which of the following is an example of an equation with no solution?

A). 4x + 3 = 3x + 3

B). 3x + 4 = 4x + 3

c). 3x + 4 = 3x + 4

D). 3x +4 = 3x + 3
Answered by Just-A-V3nter
Which of the following is an example of an equation with exactly one solution?

A). 3x + 4 = 4x + 3

B). 3x + 4 = 3x + 4

C). 4x + 3 = 4x + 3

D). 3x + 4 = 3x + 3
Answered by GPT-4o mini
To determine which of the given equations has no solution, let's analyze each option step-by-step.

A) \( 4x + 3 = 3x + 3 \)

Subtract \( 3x \) from both sides:

\( 4x - 3x + 3 = 3 \)

This simplifies to:

\( x + 3 = 3 \)

Now subtract 3 from both sides:

\( x = 0 \)

This equation has a solution (\( x = 0 \)).

---

B) \( 3x + 4 = 4x + 3 \)

Subtract \( 3x \) from both sides:

\( 4 = x + 3 \)

Subtract 3 from both sides:

\( 1 = x \)

This equation has a solution (\( x = 1 \)).

---

C) \( 3x + 4 = 3x + 4 \)

This equation is true for all values of \( x \), indicating an infinite number of solutions, not no solution.

---

D) \( 3x + 4 = 3x + 3 \)

Subtract \( 3x \) from both sides:

\( 4 = 3 \)

This statement is false, meaning there is no value of \( x \) that can satisfy the equation.

---

Thus, the correct answer is:

**D) \( 3x + 4 = 3x + 3 \)**, which has no solution.
Answered by GPT-4o mini
To determine which of the given equations has exactly one solution, let's analyze each option step-by-step:

A) \( 3x + 4 = 4x + 3 \)

Subtract \( 3x \) from both sides:

\[ 4 = x + 3 \]

Now, subtract 3 from both sides:

\[ 1 = x \]

This equation has a solution (\( x = 1 \)), which is exactly one solution.

---

B) \( 3x + 4 = 3x + 4 \)

This equation is always true for any value of \( x \), meaning there are infinitely many solutions, not exactly one solution.

---

C) \( 4x + 3 = 4x + 3 \)

Similar to option B, this equation is also always true for any value of \( x \), indicating infinitely many solutions.

---

D) \( 3x + 4 = 3x + 3 \)

Subtract \( 3x \) from both sides:

\[ 4 = 3 \]

This statement is false, meaning there is no value of \( x \) that can satisfy the equation, indicating no solutions.

---

Thus, the correct answer is:

**A) \( 3x + 4 = 4x + 3 \)**, which has exactly one solution (\( x = 1 \)).