Question
Plug in x=2 and x=-3 for both of the original equations to show that the equations
will have no solutions. Explain your work.
2x + 3 = 2x + 7
5x + 5 = 5x + 4
No special charatcters please. I want to cpy and paste
will have no solutions. Explain your work.
2x + 3 = 2x + 7
5x + 5 = 5x + 4
No special charatcters please. I want to cpy and paste
Answers
GPT-4o mini
To show that the equations will have no solutions, we will plug in x = 2 and x = -3 into both of the original equations and see if the left side equals the right side.
1. For the first equation:
2x + 3 = 2x + 7
- When x = 2:
Left side: 2(2) + 3 = 4 + 3 = 7
Right side: 2(2) + 7 = 4 + 7 = 11
Since 7 ≠ 11, this shows that for x = 2, the equation does not hold.
- When x = -3:
Left side: 2(-3) + 3 = -6 + 3 = -3
Right side: 2(-3) + 7 = -6 + 7 = 1
Since -3 ≠ 1, this shows that for x = -3, the equation also does not hold.
2. For the second equation:
5x + 5 = 5x + 4
- When x = 2:
Left side: 5(2) + 5 = 10 + 5 = 15
Right side: 5(2) + 4 = 10 + 4 = 14
Since 15 ≠ 14, this shows that for x = 2, the equation does not hold.
- When x = -3:
Left side: 5(-3) + 5 = -15 + 5 = -10
Right side: 5(-3) + 4 = -15 + 4 = -11
Since -10 ≠ -11, this shows that for x = -3, the equation also does not hold.
In conclusion, for both equations, neither x = 2 nor x = -3 yields equal values for the left and right sides, confirming that the equations have no solutions.
1. For the first equation:
2x + 3 = 2x + 7
- When x = 2:
Left side: 2(2) + 3 = 4 + 3 = 7
Right side: 2(2) + 7 = 4 + 7 = 11
Since 7 ≠ 11, this shows that for x = 2, the equation does not hold.
- When x = -3:
Left side: 2(-3) + 3 = -6 + 3 = -3
Right side: 2(-3) + 7 = -6 + 7 = 1
Since -3 ≠ 1, this shows that for x = -3, the equation also does not hold.
2. For the second equation:
5x + 5 = 5x + 4
- When x = 2:
Left side: 5(2) + 5 = 10 + 5 = 15
Right side: 5(2) + 4 = 10 + 4 = 14
Since 15 ≠ 14, this shows that for x = 2, the equation does not hold.
- When x = -3:
Left side: 5(-3) + 5 = -15 + 5 = -10
Right side: 5(-3) + 4 = -15 + 4 = -11
Since -10 ≠ -11, this shows that for x = -3, the equation also does not hold.
In conclusion, for both equations, neither x = 2 nor x = -3 yields equal values for the left and right sides, confirming that the equations have no solutions.