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

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:

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

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

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 \(x = 1\)).

which of the following is an example of an equation with one none or infinite solutions

3(x+2)-6=3x

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.

which of the following is an example of an equation with one none or infinite solutions

4x=3(x+5)-15

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 \(x = 0\)).

which of the following is an example of an equation with one none or infinite solutions

5(2x+2)-7x=3x+6

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**.

5/5 ty!

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