Answer:
First Equation → y = 21/4
Second Equation → x = -1/57
Explanation:
solving equation #1
step 1 - simplify
[tex]\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}[/tex]
step 3 - multiply each side of the equation by six
[tex]\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[/tex]
step 4 - add three to both sides of the equation.
[tex]y - 3 = 18 - 3y\\\\y-3+3=18+3-3y\\\\y = -3y+21[/tex]
step 5 - add three y to both sides of the equation.
[tex]y = -3y+21\\\\y+3y = -3y+3y+21\\\\y+3y=21[/tex]
step 6 - simplify
[tex]y+3y=21\\\\4y=21[/tex]
step 7 - divide both sides of the equation by four
[tex]4y=21\\\\\displaystyle\frac{4y}{4} = \displaystyle\frac{21}{4}\\ \\y = \displaystyle\frac{21}{4}[/tex]
Therefore, the solution to the first given equation is y = 21/4 or y = 5.25.
solving equation #2
step 1 - simplify.
[tex]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}[/tex]
step 2 - multiply each side of the equation by five.
[tex]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[/tex]
step 3 - subtract twenty x from each side of the equation.
[tex]20x + \displaystyle\frac{1}{3} = x \\\\20x -20x+ \displaystyle\frac{1}{3} = x -20x\\\\\displaystyle\frac{1}{3} = -19x[/tex]
step 4 - divide each side of the equation by negative nineteen.
[tex]\displaystyle\frac{1}{3} = -19x\\\\\displaystyle\frac{\displaystyle\frac{1}{3} }{-19} = \displaystyle\frac{-19x}{-19} \\\\-\displaystyle\frac{1}{57} = x[/tex]
step 5 - switch
[tex]-\displaystyle\frac{1}{57} =x\\\\x = -\displaystyle\frac{1}{57}[/tex]
Therefore, the solution to the second equation is x = -1/57.
