Question

Which of the following is an example of an equation with exactly one solution? (1 point)

3x + 4 = 4x + 3

3x + 4 = 3x + 4

4x + 3 =4x + 3

3x + 4 = 3x + 3

Answer 1

[AI-generated answer — Bot GPT 3.5]

3x + 4 = 4x + 3 is an example of an equation with exactly one solution.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which equation has exactly one solution, we need to set up the equations and simplify them.

Let's analyze each equation:

1) 3x + 4 = 4x + 3:
To solve this equation, we need to bring all the terms containing x to one side of the equation by subtracting 3x from both sides:
3x + 4 - 3x = 4x + 3 - 3x
4 = x + 3

2) 3x + 4 = 3x + 4:
No matter where we move the terms around, the equation always remains the same, which means all the terms on both sides of the equation are equal. Therefore, every value of x will satisfy this equation, making it an identity.

3) 4x + 3 = 4x + 3:
Similar to the previous equation, no matter how we arrange the terms, the equation remains true for all values of x. Hence, it is also an identity.

4) 3x + 4 = 3x + 3:
To isolate x, we can subtract 3 from both sides:
3x + 4 - 3 = 3x + 3 - 3
3x + 1 = 3x
Here, we have a variable on both sides, but we also have a constant value (1) on the left side. Since the left side does not simplify further, we cannot eliminate the variable entirely. This means we cannot find a single value for x that satisfies the equation.

Out of the given options, only the equation in choice number 4 (3x + 4 = 3x + 3) does not have exactly one solution.

Answer 3

[AI-generated answer — Explain Bot]

To determine which of the given equations has exactly one solution, we need to examine the coefficients and constants on both sides of the equation.

Let's go through each equation:

1. 3x + 4 = 4x + 3
To find the solution, we need to simplify both sides of the equation. By subtracting 3x from both sides, we get:
3x - 3x + 4 = 4x - 3x + 3
Simplifying further, we have 4 = x + 3.
By subtracting 3 from both sides, we obtain 4 - 3 = x, which simplifies to 1 = x.
Therefore, this equation has exactly one solution, x = 1.

2. 3x + 4 = 3x + 4
By subtracting 3x from both sides, we have 3x - 3x + 4 = 3x - 3x + 4.
Simplifying, we get 4 = 4.
In this case, both sides of the equation are identical, resulting in infinitely many solutions. This equation does not have exactly one solution.

3. 4x + 3 = 4x + 3
Similar to the previous equation, subtracting 4x from both sides yields 4x - 4x + 3 = 4x - 4x + 3.
Simplifying gives us 3 = 3.
Like before, since both sides are identical, this equation has infinitely many solutions and not exactly one solution.

4. 3x + 4 = 3x + 3
By subtracting 3x from both sides, we have 3x - 3x + 4 = 3x - 3x + 3.
Simplifying gives us 4 = 3.
Since 4 does not equal 3, there is no solution for this equation.

In summary, out of the given options, only equation 1 has exactly one solution: 3x + 4 = 4x + 3, which gives x = 1.