Ask a New Question
Menu

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

9 answers

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.

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

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.

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.

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.

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.

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: \( x = 0 \).

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.

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.