Explanation:
3u + 40 + 2u = 6u - 30 - u
5u + 40 = 5u - 30
40 = -30
that is never right this has no solution at all.
2.2z + 3z = 4.5 - 3.2
5.2z = 1.3
z = 1.3/5.2 = 0.25 or 1/4
this has exactly one solution.
(4/5)x + 2/3 + (1/5)x = x
4/5 + 1/5 = 5/5 = 1/1 = 1, so
x + 2/3 = x
2/3 = 0
that is never right this has no solution at all.
2.3y + 3.2 - y = 2.1 + 1.3y + 1.1
1.3y + 3.2 = 1.3y + 3.2
3.2 = 3.2
this is always correct, no matter what numbers we use for y.
so, this has infinitely many solutions
(2/3)x + 2/3 + (1/5)x = 2/3x
2/3 + (1/5)x = 0
(1/5)x = -2/3
x = -2/3 / 1/5 = (-2×5)/(3×1) = -10/3
this has exactly one solution.
20 + 4r = 32 - 2r
20 + 6r = 32
6r = 12
r = 2
this has exactly one solution.