which of the following is an example of an equation with no solution

Question

3x+4=3x+3
3x+4=3x+4
3x+4=4x+3
4x+3=3x+3

Answer 1

To determine which of the given equations has no solution, we need to analyze each equation:

1. Equation 1: \(3x + 4 = 3x + 3\)

   Subtracting \(3x\) from both sides gives: \[ 4 = 3 \] This is false. Therefore, this equation has no solution.

2. Equation 2: \(3x + 4 = 3x + 4\)

   Subtracting \(3x + 4\) from both sides gives: \[ 0 = 0 \] This is true for all \(x\). Therefore, this equation has infinitely many solutions.

3. Equation 3: \(3x + 4 = 4x + 3\)

   Rearranging gives: \[ 3x + 4 - 4x = 3 \implies -x + 4 = 3 \implies -x = -1 \implies x = 1 \] This has one solution (x = 1).

4. Equation 4: \(4x + 3 = 3x + 3\)

   Rearranging gives: \[ 4x - 3x + 3 = 3 \implies x + 3 = 3 \implies x = 0 \] This also has one solution (x = 0).

Based on the analysis, the equation with no solution is:

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

Answer 2

which of the following is an example of an equation with exactly one solution
4x+3=4x+3
3x+4=4x+3
3x+4=3x+4
3x+4=3x+3

Answer 3

To identify which of the given equations has exactly one solution, we’ll analyze each equation:

1. Equation 1: \(4x + 3 = 4x + 3\)

   Subtracting \(4x + 3\) from both sides gives: \[ 0 = 0 \] This equation is true for all \(x\) and thus has infinitely many solutions, not just one.

2. Equation 2: \(3x + 4 = 4x + 3\)

   Rearranging gives: \[ 3x - 4x + 4 = 3 \implies -x + 4 = 3 \implies -x = -1 \implies x = 1 \] This equation has exactly one solution (x = 1).

3. Equation 3: \(3x + 4 = 3x + 4\)

   Subtracting \(3x + 4\) from both sides gives: \[ 0 = 0 \] Like the first equation, this one is true for all \(x\) and has infinitely many solutions.

4. Equation 4: \(3x + 4 = 3x + 3\)

   Subtracting \(3x\) from both sides gives: \[ 4 = 3 \] This is false and indicates that there is no solution, not just one.

Based on the analysis, the equation with exactly one solution is:

\(3x + 4 = 4x + 3\) (with the solution \(x = 1\)).

Answer 4

which of the following is an example of an equation with one none or infinite solutions
3(x+2)-6=3x

Answer 5

To determine the number of solutions for the equation \(3(x + 2) - 6 = 3x\), we will simplify and solve it step-by-step.

1. Distribute the \(3\) on the left-hand side: \[ 3(x + 2) - 6 = 3x \implies 3x + 6 - 6 = 3x \]

2. Simplify the left-hand side: \[ 3x + 6 - 6 = 3x \implies 3x = 3x \]

Now, the equation simplifies to: \[ 3x = 3x \]

This is true for all values of \(x\). Therefore, the equation represents an identity and has infinitely many solutions.

Conclusion: The equation \(3(x + 2) - 6 = 3x\) has infinitely many solutions.

Answer 6

which of the following is an example of an equation with one none or infinite solutions
4x=3(x+5)-15

Answer 7

To determine the number of solutions for the equation \(4x = 3(x + 5) - 15\), we will simplify and solve it step-by-step.

1. Distribute the \(3\) on the right side: \[ 3(x + 5) = 3x + 15 \] So the equation becomes: \[ 4x = 3x + 15 - 15 \]

2. Simplify the equation: \[ 4x = 3x + 0 \implies 4x = 3x \]

3. Subtract \(3x\) from both sides: \[ 4x - 3x = 0 \implies x = 0 \]

Now we have found one specific solution, \(x = 0\).

Conclusion: The equation \(4x = 3(x + 5) - 15\) has exactly one solution (which is \(x = 0\)).

Answer 8

which of the following is an example of an equation with one none or infinite solutions
5(2x+2)-7x=3x+6

Answer 9

To determine the number of solutions for the equation \(5(2x + 2) - 7x = 3x + 6\), we'll simplify and solve it step-by-step.

1. Distribute on the left side: \[ 5 \cdot 2x + 5 \cdot 2 - 7x = 3x + 6 \ 10x + 10 - 7x = 3x + 6 \]

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

3. Move \(3x\) from both sides: \[ 3x + 10 - 3x = 3x + 6 - 3x \ 10 = 6 \]

This statement, \(10 = 6\), is false.

Since we ended up with a false statement, this means the equation has no solution.

Conclusion: The equation \(5(2x + 2) - 7x = 3x + 6\) has no solutions.

Answer 10

5/5 ty!

Answer 11

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying! 😊