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TEA [102]
3 years ago
11

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

Mathematics
1 answer:
kogti [31]3 years ago
5 0

<u>Answer:</u>

<em>First Equation → </em><u><em>y = 21/4</em></u>

<em>Second Equation → </em><u><em>x = -1/57</em></u>

<u />

<u>Explanation:</u>

<em>solving equation #1</em>

<em></em>

step 1 - simplify

<em></em>

\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 <u><em>y = 21/4 </em></u><em>or y = 5.25.</em>

<u><em /></u>

<em>solving equation #2</em>

<em />

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 <em><u>x = -1/57.</u></em>

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