Question

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

Answer 1

Answer:

First Equation → y = 21/4

Second Equation → x = -1/57

Explanation:

solving equation #1

step 1 - simplify

$\displaystyle\frac{1}{6}y - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{1}{2}y\\\\\displaystyle\frac{1}{6}* \displaystyle\frac{y}{1} - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{1}{2}* \displaystyle\frac{y}{1}\\\\\displaystyle\frac{y}{6} - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{y}{2}$

step 3 - multiply each side of the equation by six

$\displaystyle\frac{y}{6} - \displaystyle\frac{1}{2} = 3 - \displaystyle\frac{y}{2}\\\\\displaystyle\frac{y}{6} * \displaystyle\frac{6}{1}- \displaystyle\frac{1}{2} * \displaystyle\frac{6}{1}= \displaystyle\frac{3}{1} *\displaystyle\frac{6}{1} - \displaystyle\frac{y}{2}* \displaystyle\frac{6}{1}\\\\y - 3 = 18 - 3y$

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

$4y=21\\\\\displaystyle\frac{4y}{4} = \displaystyle\frac{21}{4}\\ \\y = \displaystyle\frac{21}{4}$

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

solving equation #2

step 1 - simplify.

$4x + \displaystyle\frac{1}{15} = \displaystyle\frac{2x}{10} \\\\4x + \displaystyle\frac{1}{15} = 2*\displaystyle\frac{x}{10}\\\\4x+\displaystyle\frac{1}{15} = \displaystyle\frac{x}{5}$

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

$4x+\displaystyle\frac{1}{15} = \displaystyle\frac{x}{5}\\\\\displaystyle\frac{4x}{1}* \displaystyle\frac{5}{1} +\displaystyle\frac{1}{15} * \displaystyle\frac{5}{1} = \displaystyle\frac{x}{5}* \displaystyle\frac{5}{1} \\\\20x + \displaystyle\frac{1}{3} = x$

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

$20x + \displaystyle\frac{1}{3} = x \\\\20x -20x+ \displaystyle\frac{1}{3} = x -20x\\\\\displaystyle\frac{1}{3} = -19x$

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

$\displaystyle\frac{1}{3} = -19x\\\\\displaystyle\frac{\displaystyle\frac{1}{3} }{-19} = \displaystyle\frac{-19x}{-19} \\\\-\displaystyle\frac{1}{57} = x$

step 5 - switch

$-\displaystyle\frac{1}{57} =x\\\\x = -\displaystyle\frac{1}{57}$

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