Which equations have no solutions? Select two correct answers.*1 point-4x = 3x4x -1 = 1- 4x4x + 6 = 6 + 4x-4x + 1 = 5 - 4x4x - 1= 2 (2x-1)
Question
Which equations have no solutions? Select two correct answers.*1 point-4x = 3x4x -1 = 1- 4x4x + 6 = 6 + 4x-4x + 1 = 5 - 4x4x - 1= 2 (2x-1)
Solution
The equations that have no solutions are:
- 4x -1 = 1 - 4x
- 4x - 1= 2 (2x-1)
Let's break it down:
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For the equation 4x -1 = 1 - 4x, if we add 4x to both sides, we get 4x + 4x - 1 = 1, which simplifies to 8x - 1 = 1. If we add 1 to both sides, we get 8x = 2, and if we divide both sides by 8, we get x = 2/8 = 0.25. However, if we substitute x = 0.25 back into the original equation, we get 4(0.25) - 1 ≠ 1 - 4(0.25), which means the equation has no solution.
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For the equation 4x - 1= 2 (2x-1), if we distribute the 2 on the right side, we get 4x - 1 = 4x - 2. If we subtract 4x from both sides, we get -1 ≠ -2, which means the equation has no solution.
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