Question

1/5x + 1/2 = 3 + 1/2xSolve for x.

Answer 1

`x=-8(1)/(3)`

Step-by-step explanation:

Given the equation

`(1)/(5)x+(1)/(2)=3+(1)/(2)x`

We begin by collecting like terms as follows:

`(1)/(5)x-(1)/(2)x=3-(1)/(2)`

Next, we take the lowest common multiples of the denominator on each side.

`\begin{gathered} (2x-5x)/(10)=(6-1)/(2) \\ -(3x)/(10)=(5)/(2) \end{gathered}`

We cross-multiply

`\begin{gathered} -3x*2=10*5 \\ -6x=50 \end{gathered}`

Finally, apply the division rule of equality.

`\begin{gathered} -(6x)/(-6)=(50)/(-6) \\ x=-8(2)/(6) \\ x=-8(1)/(3) \end{gathered}`