Answer:
options (a), (b), (c), and (e) have the same solution as the solution of 3/5 x + 2/3 + x = 1/2 -1/5x.
Explanation:
The given equation is
3/5 x + 2/3 + x = 1/2 -1/5x
First, rearrange the equation to have constant terms and the terms having variable on the separate side.
3/5 x + x +1/5x= 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 ...(i)
Now, find the solution of all the options in the similar way:
(a) 8/5 x +2/3 = 1/2 -1/5 x
8/5 x + 1/5 x = 1/2 - 2/3
9/5 x = -1/6
x= -1/6 ÷ 9/5
x= -1/6 x 5/9
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(b) 18x + 20 + 30x = 15 – 6x
18x+30x+6x = 15 -20
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [from equation (i)]
(c) 18x + 20 + x = 15 – 6x
18x+x+6x = 15 -20
25x=-5
x= -5/25 which is not the same as the solution of the mentioned equation. [ from equation (i)]
(d) 24x + 30x = –5
54x = -5
54x=-5
x= -5/54 which is same as the solution of the mentioned equation. [ from equation (i)]
(e) 12x + 30x = –5
42x = -5
42x=-5
x= -5/42 which not is same as the solution of the mentioned equation. [ from equation (i)].
Hence, options (a), (b), (c), and (e) have the same solution as the solutions of the given equation.