Question

Which equations have the same solution as x + + x = – x plus StartFraction 2 Over 3 EndFraction plus x equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.

Answer 1

A, B and D

Explanation:

Which equations have the same solution as
`(3)/(5) x+(2)/(3) +x=(1)/(2) -(1)/(5)x`

A. 8/5x + 2/3 = 1/2 – 1/5x

B. 18x + 20 + 30x = 15 – 6x

C. 18x + 20 + x = 15 – 6x

D. 24x + 30x = –5

E. 12x + 30x = –5

To find the equations with the same solution, we have to solve or x and determine if the value of x is the same for the remaining options.

`(3)/(5) x+(2)/(3) +x=(1)/(2) -(1)/(5)x\\multipying \ through \ by \ 30:\\18x + 20+30x=15-6x\\collecting\ like\ terms:\\18x+30x+6x=15-20\\54x=-5\\x=(-5)/(54)`

A)

`(8)/(5)x+(2)/(3)=(1)/(2)-(1)/(5)x\\ multipying\ through\ by \ 30\ gives:\\48x+20=15-6x\\48x+6x=15-20\\54x=-5\\x=(-5)/(54)`

A has the same solution

B)

`18x+20+30x=15-6x\\18x+30x+6=15-20\\54x=-5\\x=(-5)/(54)`

B has the same solution

C)

`18x+20+x=15-6x\\18x+x+6x=15-20\\25x=-5\\x=(-1)/(5)`

C do not have the same solution

D)

`24x+30x=-5\\54x=-5\\x=(-5)/(54)`

D has the same solution

E)

`12x+30x=-5\\42x=-5\\x=(-5)/(42\\)`

E do not have the same solution