Question

Solve: 1. 1/6y− 1/2 =3− 1/2y 2. 4x+1/15 = 2x/10

Answer 1

First Equation → y = 21/4

Second Equation → x = -1/57

Step-by-step explanation:

solving equation #1

step 1 - simplify

`\displaystyle(1)/(6)y - \displaystyle(1)/(2) = 3 - \displaystyle(1)/(2)y\\\\\displaystyle(1)/(6)* \displaystyle(y)/(1) - \displaystyle(1)/(2) = 3 - \displaystyle(1)/(2)* \displaystyle(y)/(1)\\\\\displaystyle(y)/(6) - \displaystyle(1)/(2) = 3 - \displaystyle(y)/(2)`

step 3 - multiply each side of the equation by six

`\displaystyle(y)/(6) - \displaystyle(1)/(2) = 3 - \displaystyle(y)/(2)\\\\\displaystyle(y)/(6) * \displaystyle(6)/(1)- \displaystyle(1)/(2) * \displaystyle(6)/(1)= \displaystyle(3)/(1) *\displaystyle(6)/(1) - \displaystyle(y)/(2)* \displaystyle(6)/(1)\\\\y - 3 = 18 - 3y`

step 4 - add three to both sides of the equation.

`y - 3 = 18 - 3y\\\\y-3+3=18+3-3y\\\\y = -3y+21`

step 5 - add three y to both sides of the equation.

`y = -3y+21\\\\y+3y = -3y+3y+21\\\\y+3y=21`

step 6 - simplify

`y+3y=21\\\\4y=21`

step 7 - divide both sides of the equation by four

`4y=21\\\\\displaystyle(4y)/(4) = \displaystyle(21)/(4)\\ \\y = \displaystyle(21)/(4)`

Therefore, the solution to the first given equation is y = 21/4 or y = 5.25.

solving equation #2

step 1 - simplify.

`4x + \displaystyle(1)/(15) = \displaystyle(2x)/(10) \\\\4x + \displaystyle(1)/(15) = 2*\displaystyle(x)/(10)\\\\4x+\displaystyle(1)/(15) = \displaystyle(x)/(5)`

step 2 - multiply each side of the equation by five.

`4x+\displaystyle(1)/(15) = \displaystyle(x)/(5)\\\\\displaystyle(4x)/(1)* \displaystyle(5)/(1) +\displaystyle(1)/(15) * \displaystyle(5)/(1) = \displaystyle(x)/(5)* \displaystyle(5)/(1) \\\\20x + \displaystyle(1)/(3) = x`

step 3 - subtract twenty x from each side of the equation.

`20x + \displaystyle(1)/(3) = x \\\\20x -20x+ \displaystyle(1)/(3) = x -20x\\\\\displaystyle(1)/(3) = -19x`

step 4 - divide each side of the equation by negative nineteen.

`\displaystyle(1)/(3) = -19x\\\\\displaystyle(\displaystyle(1)/(3) )/(-19) = \displaystyle(-19x)/(-19) \\\\-\displaystyle(1)/(57) = x`

step 5 - switch

`-\displaystyle(1)/(57) =x\\\\x = -\displaystyle(1)/(57)`

Therefore, the solution to the second equation is x = -1/57.