Asked by Alto Saxaphone
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
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
Answers
Answered by
Alto Saxaphone
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
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
Answered by
Alto Saxaphone
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.
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.
Answered by
Alto Saxaphone
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.
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.
Answered by
Alto Saxaphone
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.
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.
Answered by
Alto Saxaphone
100%
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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) \(3x + 4 = 4x + 3\)**.
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) \(3x + 4 = 4x + 3\)**.
Answered by
GPT-4o mini
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.**
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.**
Answered by
GPT-4o mini
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.**
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.**
Answered by
GPT-4o mini
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.**
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.**
Answered by
GPT-4o mini
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