Question

Which of the following is an example of an equation with no solution?(1 point)
Responses

a) 3x+4=3x+3
3 x plus 4 equals 3 x plus 3

b) 3x+4=4x+3
3 x plus 4 equals 4 x plus 3

c) 4x+3=3x+3
4 x plus 3 equals 3 x plus 3

d) 3x+4=3x+4

Answer 1

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

3x+4=3x+4
3 x plus 4 equals 3 x plus 4

3x+4=3x+3
3 x plus 4 equals 3 x plus 3

4x+3=4x+3
4 x plus 3 equals 4 x plus 3

3x+4=4x+3
3 x plus 4 equals 4 x plus 3

Answer 2

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.

Answer 3

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 one solution: x=0.
The equation has one solution: x equals 0 .

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.

Answer 4

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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=10.
The equation has one solution: x equals 10 .

The equation has one solution: x=6.
The equation has one solution: x equals 6 .

The equation has no solution.

Answer 5

100%

Answer 6

To determine which equation has no solution, we need to analyze each option:

a) \(3x + 4 = 3x + 3\)
Subtract \(3x\) from both sides:
\(4 = 3\) (false statement, hence no solution)

b) \(3x + 4 = 4x + 3\)
Subtract \(3x\) from both sides:
\(4 = x + 3\)
Solve for \(x\):
\(x = 1\) (has a solution)

c) \(4x + 3 = 3x + 3\)
Subtract \(3x\) from both sides:
\(x + 3 = 3\)
Solve for \(x\):
\(x = 0\) (has a solution)

d) \(3x + 4 = 3x + 4\)
This is an identity (true for all \(x\), hence infinite solutions)

Based on this analysis, option **a) \(3x+4=3x+3\)** is an example of an equation with no solution.

Answer 7

To find the equation with exactly one solution, let's analyze each option:

1) \(3x + 4 = 3x + 4\)
This equation is true for all \(x\) (identity), resulting in infinite solutions.

2) \(3x + 4 = 3x + 3\)
Subtract \(3x\) from both sides:
\(4 = 3\), which is a false statement, leading to no solution.

3) \(4x + 3 = 4x + 3\)
This is also an identity, true for all \(x\), resulting in infinite solutions.

4) \(3x + 4 = 4x + 3\)
Subtract \(3x\) from both sides:
\(4 = x + 3\)
Solve for \(x\):
\(x = 1\), which means there is exactly one solution.

Based on this analysis, the equation with exactly one solution is option **4) \(3x + 4 = 4x + 3\)**.

Answer 8

Let's solve the equation \(3(x+2)−6=3x\) step-by-step:

1. Start with the equation:
\[
3(x + 2) - 6 = 3x
\]

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

3. Simplify the left side:
\[
3x = 3x
\]

At this point, we have \(3x = 3x\), which is a true statement for all values of \(x\).

Since the left side and the right side are equal for all \(x\), the equation has **infinite solutions**.

Therefore, the correct response is:
**The equation has infinite solutions.**

Answer 9

Let's solve the equation \(4x = 3(x + 5) - 15\) step-by-step:

1. Start with the equation:
\[
4x = 3(x + 5) - 15
\]

2. Expand the right side:
\[
4x = 3x + 15 - 15
\]

3. Simplify the right side:
\[
4x = 3x + 0
\]
\[
4x = 3x
\]

4. Now, subtract \(3x\) from both sides:
\[
4x - 3x = 0
\]
\[
x = 0
\]

Since we found a specific solution \(x = 0\), the equation has **one solution**.

Thus, the correct response is:
**The equation has one solution: x=0.**

Answer 10

Let's solve the equation \(5(2x + 2) - 7x = 3x + 6\) step by step.

1. Start with the equation:
\[
5(2x + 2) - 7x = 3x + 6
\]

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

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

4. Subtract \(3x\) from both sides:
\[
10 = 6
\]

This is a false statement (10 does not equal 6), which means there are **no solutions** to this equation.

Thus, the correct response is:
**The equation has no solution.**

Answer 11

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