Question
What two equations have infinite solutions?
2x+3=2x+7
7x+3=7x+3
4x+22=8x+10
5x+5=5x+4
3x+18=5x+8
3(4x+8)=4(3x+6)
check your work
2x+3=2x+7
7x+3=7x+3
4x+22=8x+10
5x+5=5x+4
3x+18=5x+8
3(4x+8)=4(3x+6)
check your work
Answers
GPT 3.5
The first equation, 2x+3=2x+7, has no solutions since the variable x is eliminated when subtracting 2x from both sides. Therefore, this equation does not have infinite solutions.
The second equation, 7x+3=7x+3, is an identity. It means that both sides of the equation are equal for every value of x. Therefore, this equation has infinite solutions.
The third equation, 4x+22=8x+10, has one solution. By simplifying and solving for x, we find x = 3.
The fourth equation, 5x+5=5x+4, has no solutions since the variable x is eliminated when subtracting 5x from both sides. Therefore, this equation does not have infinite solutions.
The fifth equation, 3x+18=5x+8, has one solution. By simplifying and solving for x, we find x = 5.
The sixth equation, 3(4x+8)=4(3x+6), can be simplified to 12x+24=12x+24. This is an identity, similar to the second equation. Therefore, this equation has infinite solutions.
Checking the work, we find that the second and sixth equations have infinite solutions.
The second equation, 7x+3=7x+3, is an identity. It means that both sides of the equation are equal for every value of x. Therefore, this equation has infinite solutions.
The third equation, 4x+22=8x+10, has one solution. By simplifying and solving for x, we find x = 3.
The fourth equation, 5x+5=5x+4, has no solutions since the variable x is eliminated when subtracting 5x from both sides. Therefore, this equation does not have infinite solutions.
The fifth equation, 3x+18=5x+8, has one solution. By simplifying and solving for x, we find x = 5.
The sixth equation, 3(4x+8)=4(3x+6), can be simplified to 12x+24=12x+24. This is an identity, similar to the second equation. Therefore, this equation has infinite solutions.
Checking the work, we find that the second and sixth equations have infinite solutions.
What two have no solutions?
2x+3=2x+7
7x+3=7x+3
4x+22=8x+10
5x+5=5x+4
3x+18=5x+8
3(4x+8)=4(3x+6)
Check your work.
2x+3=2x+7
7x+3=7x+3
4x+22=8x+10
5x+5=5x+4
3x+18=5x+8
3(4x+8)=4(3x+6)
Check your work.
GPT 3.5
Apologies for the previous mistakes. Let's re-evaluate the equations:
The first equation, 2x+3=2x+7, simplifies to 0=4, which is not true. Therefore, this equation has no solutions.
The second equation, 7x+3=7x+3, is an identity. It means that both sides of the equation are equal for every value of x. Therefore, this equation has infinite solutions.
The third equation, 4x+22=8x+10, simplifies to 0=12, which is not true. Therefore, this equation has no solutions.
The fourth equation, 5x+5=5x+4, simplifies to 1=4, which is not true. Therefore, this equation has no solutions.
The fifth equation, 3x+18=5x+8, can be simplified to -2 = 2x. Solving for x, we get x = -1. Therefore, this equation has a single solution, not no solutions.
The sixth equation, 3(4x+8)=4(3x+6), can be further simplified to 12x + 24 = 12x + 24. This is another identity, similar to the second equation. Therefore, this equation has infinite solutions.
To summarize, the first, third, and fourth equations have no solutions, while the second and sixth equations have infinite solutions. The fifth equation has a single solution.
The first equation, 2x+3=2x+7, simplifies to 0=4, which is not true. Therefore, this equation has no solutions.
The second equation, 7x+3=7x+3, is an identity. It means that both sides of the equation are equal for every value of x. Therefore, this equation has infinite solutions.
The third equation, 4x+22=8x+10, simplifies to 0=12, which is not true. Therefore, this equation has no solutions.
The fourth equation, 5x+5=5x+4, simplifies to 1=4, which is not true. Therefore, this equation has no solutions.
The fifth equation, 3x+18=5x+8, can be simplified to -2 = 2x. Solving for x, we get x = -1. Therefore, this equation has a single solution, not no solutions.
The sixth equation, 3(4x+8)=4(3x+6), can be further simplified to 12x + 24 = 12x + 24. This is another identity, similar to the second equation. Therefore, this equation has infinite solutions.
To summarize, the first, third, and fourth equations have no solutions, while the second and sixth equations have infinite solutions. The fifth equation has a single solution.