Use properties to rewrite the given equation. which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? check all that apply. 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

we have

Combine like terms in both sides

we know that

substitute in the expression above

-----> equation A        

Multiply equation A by both sides

---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

---------> equation C

Solve for x

We are going to proceed to verify each case to determine the solution.

Case a)

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

Case b)

Combine like terms in left side

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

Case c)

Combine like terms in left side

therefore

the case c) not have the same solution that the given equation

Case d)

Combine like terms in left side

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

Case e)

Combine like terms in left side

therefore

the case e) not have the same solution that the given equation

therefore

the answer is

case a)

case b)

case d)

the answer is 1/4

step-by-step explanation: