1/7(7/8y+7)-3/4(2/9y+1 7/9)=1/12

3 min read Jun 16, 2024

Solving Algebraic Equation: 1/7(7/8y+7)-3/4(2/9y+17/9)=1/12

In this article, we will solve the algebraic equation:

1/7(7/8y+7) - 3/4(2/9y+17/9) = 1/12

Step 1: Simplify the equation

Let's start by simplifying the equation. We can do this by evaluating the expressions inside the parentheses:

1/7(7/8y + 7) = 1/7(7/8y) + 1/7(7) = 1/8y + 1 -3/4(2/9y + 17/9) = -3/4(2/9y) - 3/4(17/9) = -6/36y - 51/36

Now, substitute these expressions back into the original equation:

1/8y + 1 - 6/36y - 51/36 = 1/12

Step 2: Combine like terms

Combine like terms to simplify the equation further:

1/8y - 6/36y - 51/36 + 1 = 1/12

Combine the fractions:

(18-6)/36y - 51/36 + 1 = 1/12

(12/36)y - 51/36 + 1 = 1/12

(1/3)y - 51/36 + 1 = 1/12

Step 3: Solve for y

Now, solve for y by adding 51/36 to both sides of the equation:

(1/3)y - 51/36 + 1 = 1/12

(1/3)y - 51/36 + 51/36 = 1/12 + 51/36

(1/3)y + 1 = 63/36 + 51/36

(1/3)y + 1 = 114/36

Subtract 1 from both sides:

(1/3)y = 114/36 - 1

(1/3)y = (114-36)/36

(1/3)y = 78/36

Multiply both sides by 3 to solve for y:

y = 78/12

y = 6.5

Therefore, the value of y is 6.5.

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