1/9(3y-27)-2(1/12y-1 5)=1/6y

Suzhoumeite

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Jun 16, 2024

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Solving Linear Equations: A Step-by-Step Guide

In this article, we will solve a linear equation involving fractions: 1/9(3y-27)-2(1/12y-1 5)=1/6y. Follow along as we break down the equation and solve for y.

Simplifying the Equation

First, let's simplify the equation by combining like terms:

$\frac{1}{9}(3y-27) - 2(\frac{1}{12}y-1 \frac{5}{12}) = \frac{1}{6}y$

Multiplying Both Sides by 36

To eliminate the fractions, we multiply both sides of the equation by 36, the least common multiple of 9, 12, and 6:

$36(\frac{1}{9}(3y-27) - 2(\frac{1}{12}y-1 \frac{5}{12})) = 36(\frac{1}{6}y)$

Expanding and Simplifying

Now, let's expand and simplify both sides of the equation:

$4(3y-27) - 6(1y-5) = 6y$ $12y - 108 - 6y + 30 = 6y$ $6y - 78 = 6y$

Solving for y

Finally, let's solve for y by adding 78 to both sides of the equation:

$6y - 78 + 78 = 6y + 78$ $6y = 78$ $y = 13$

Therefore, the value of y is 13.