solve x+9/5=3/2-x-3/4

Question

I found the LCD which is 20

 

Answer 1

x + 9/5 = 3/2 - x - 3/4

• First group terms on each side of the =

x + 9/5 = -x + 3/2 - 3/4

• Now add x to both sides to get x on the left of the equation

x + x + 9/5 = -x + x + 3/2 - 3/4

2x + 9/5 = 0 + 3/2 - 3/4

• Now subtract 9/5 from each side to get x alone

2x + 9/5 - 9/5 = 3/2 - 3/4 - 9/5

2x + 0 = 3/2 - 3/4 - 9/5

• Then change your fractions so they have the same denominator
• You are correct that the LCD is 20

2x = (3/2)(10/10) - (3/4)(5/5) - (9/5)(4/4)

2x = 30/20 - 15/20 - 36/20

• And combine like terms

2x = (30 - 15 - 36)/20

2x = -21/20

• Finally multiply both sides by ½ to solve for x

(2x)(½) = (-21/20)(½)

x = (-21)(1)/(20)(2)

x = -21/40

 

x = -21/40

 

Always check your work by replacing x in the original equation with your answer and see if both sides of the equation are equal.

Answer 2

 X + 9/5 = 3/2- X - 3/4

 

 

20 ( X + 9/ 5 ) = 20 ( 3/2 - x - 3/4 )  / Multiply both sides by 20 , LCD of all denominators.

 

 20 X + 36 = 30 - 20 X - 15

 

 40 X = -21

 

   X = -21 /40