Asked by hhbh
Which of the following equations has no solution?
7
x
−
3
x
−
4
=
4
7
x
−
3
x
+
4
=
4
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting the expressions as fractions 7/x and 3/x:
1) 7/x − 3/x − 4 = 4
=> (7−3)/x − 4 = 4
=> 4/x − 4 = 4
=> 4/x = 8
=> x = 1/2 (valid, x ≠ 0)
2) 7/x − 3/x + 4 = 4
=> (7−3)/x + 4 = 4
=> 4/x + 4 = 4
=> 4/x = 0
But 4/x = 0 has no finite solution (and x = 0 is not allowed). Therefore the second equation has no solution.
1) 7/x − 3/x − 4 = 4
=> (7−3)/x − 4 = 4
=> 4/x − 4 = 4
=> 4/x = 8
=> x = 1/2 (valid, x ≠ 0)
2) 7/x − 3/x + 4 = 4
=> (7−3)/x + 4 = 4
=> 4/x + 4 = 4
=> 4/x = 0
But 4/x = 0 has no finite solution (and x = 0 is not allowed). Therefore the second equation has no solution.
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