Identify equation and goal: Identify the equation and the goal. We are given the equation (1/4)y - 7 = (2/9)y, and we need to solve for y.Clear fractions with common denominator: Clear the fractions by finding a common denominator for the terms involving y. The common denominator for 4 and 9 is 36. Multiply each term by 36 to eliminate the fractions. 36 * (1/4)y - 36 * 7 = 36 * (2/9)yPerform multiplication: Perform the multiplication. (36/4)y - 36*7 = (36/2/9)y 9y - 252 = 4yMove terms involving y: Move all terms involving y to one side of the equation. Subtract 4y from both sides to get all the y terms on one side. 9y - 4y - 252 = 4y - 4y 5y - 252 = 0Isolate the y term: Isolate the y term. Add 252 to both sides to solve for y. 5y - 252 + 252 = 0 + 252 5y = 252Solve for y: Solve for y. Divide both sides by 5 to find the value of y. 5y/5 = 252/5 y = 50.4

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$\frac{1}{4}y-7=\frac{2}{9}y$

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Algebra 2

Evaluate rational exponents

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\frac{1}{4}y-7=\frac{2}{9}y

Identify equation and goal: Identify the equation and the goal. $\newline$ We are given the equation $(\frac{1}{4})y - 7 = (\frac{2}{9})y$ , and we need to solve for $y$ .
Clear fractions with common denominator: Clear the fractions by finding a common denominator for the terms involving $y$ . The common denominator for $4$ and $9$ is $36$ . Multiply each term by $36$ to eliminate the fractions. $36 \times (\frac{1}{4})y - 36 \times 7 = 36 \times (\frac{2}{9})y$
Perform multiplication: Perform the multiplication. $\newline$ $(\frac{36}{4})y - 36\times7 = (\frac{36}{2}/9)y$ $\newline$ $9y - 252 = 4y$
Move terms involving $y$ : Move all terms involving $y$ to one side of the equation. $\newline$ Subtract $4y$ from both sides to get all the $y$ terms on one side. $\newline$ $9y - 4y - 252 = 4y - 4y$ $\newline$ $5y - 252 = 0$
Isolate the y term: Isolate the y term. $\newline$ Add $252$ to both sides to solve for $y$ . $\newline$ $5y - 252 + 252 = 0 + 252$ $\newline$ $5y = 252$
Solve for y: Solve for y. $\newline$ Divide both sides by $5$ to find the value of $y$ . $\newline$ $\frac{5y}{5} = \frac{252}{5}$ $\newline$ $y = 50.4$