Question
Which of the equations has one solution that is 5/4? select all the apply
Answers
GPT 3.5
To determine which of the equations has a solution of 5/4, we will substitute 5/4 into each equation and check if it satisfies the equation.
1. 2x - 3 = 5/4
Substitute x = 5/4:
2(5/4) - 3 = 5/4
5/2 - 3 = 5/4
This equation is not satisfied since the left side is not equal to the right side.
2. 3x + 2 = 5/4
Substitute x = 5/4:
3(5/4) + 2 = 5/4
15/4 + 2 = 5/4
15/4 + 8/4 = 5/4
23/4 = 5/4
This equation is not satisfied since the left side is not equal to the right side.
3. (2x + 5)/4 = 5/4
Substitute x = 5/4:
(2(5/4) + 5)/4 = 5/4
(10/4 + 5)/4 = 5/4
(10/4 + 20/4)/4 = 5/4
30/4 / 4 = 5/4
7.5/4 = 5/4
This equation is satisfied since the left side is equal to the right side.
Therefore, the equation (2x + 5)/4 = 5/4 has one solution that is 5/4.
1. 2x - 3 = 5/4
Substitute x = 5/4:
2(5/4) - 3 = 5/4
5/2 - 3 = 5/4
This equation is not satisfied since the left side is not equal to the right side.
2. 3x + 2 = 5/4
Substitute x = 5/4:
3(5/4) + 2 = 5/4
15/4 + 2 = 5/4
15/4 + 8/4 = 5/4
23/4 = 5/4
This equation is not satisfied since the left side is not equal to the right side.
3. (2x + 5)/4 = 5/4
Substitute x = 5/4:
(2(5/4) + 5)/4 = 5/4
(10/4 + 5)/4 = 5/4
(10/4 + 20/4)/4 = 5/4
30/4 / 4 = 5/4
7.5/4 = 5/4
This equation is satisfied since the left side is equal to the right side.
Therefore, the equation (2x + 5)/4 = 5/4 has one solution that is 5/4.