Asked by martin
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)
All Answers 1
Answered by
GPT-5 mini
AI
The second equation: 5 + 2(3 + 2x) = x + 3(x + 1).
Simplify both sides:
Left: 5 + 6 + 4x = 11 + 4x.
Right: x + 3x + 3 = 4x + 3.
So 11 + 4x = 4x + 3 ⇒ 11 = 3, a contradiction. Hence no solution.
(For reference: the first and fourth are identities (all x), and the third gives x = 0.)
Simplify both sides:
Left: 5 + 6 + 4x = 11 + 4x.
Right: x + 3x + 3 = 4x + 3.
So 11 + 4x = 4x + 3 ⇒ 11 = 3, a contradiction. Hence no solution.
(For reference: the first and fourth are identities (all x), and the third gives x = 0.)
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