Isolate y terms: First, we need to isolate the terms with y on one side of the equation. To do this, we can add 7 to both sides of the equation to get rid of the -7 on the left side. (4)/(4)y - 7 + 7 = (2)/(9)y + 7 This simplifies to: (4)/(4)y = (2)/(9)y + 7Simplify equation: Next, we notice that (4)/(4)y simplifies to y because (4)/(4) is equal to 1. So we rewrite the equation as: y = (2)/(9)y + 7Move y terms: Now, we need to get all the y terms on one side. We can subtract (2)/(9)y from both sides to move it to the left side: y - (2)/(9)y = 7Find common denominator: To combine the y terms, we need a common denominator. Since the denominators are 1 and 9, the common denominator is 9. We can rewrite y as (9)/(9)y: (9)/(9)y - (2)/(9)y = 7Combine y terms: Now we can subtract the fractions: (9)/(9)y - (2)/(9)y = (7)/(9)y So we have: (7)/(9)y = 7Divide by (7/9): To solve for y, we can divide both sides by (7)/(9): y = 7 / ((7)/(9))Multiply by reciprocal: To divide by a fraction, we multiply by its reciprocal. The reciprocal of (7)/(9) is (9)/(7): y = 7 * (9)/(7)Simplify solution: Now we can simplify the right side by canceling out the 7s: y = 9

Precalculus

Evaluate rational exponents

Full solution

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

Isolate y terms: First, we need to isolate the terms with $y$ on one side of the equation. To do this, we can add $7$ to both sides of the equation to get rid of the $-7$ on the left side. $\newline$ $\frac{4}{4}y - 7 + 7 = \frac{2}{9}y + 7$ $\newline$ This simplifies to: $\newline$ $\frac{4}{4}y = \frac{2}{9}y + 7$
Simplify equation: Next, we notice that $(4)/(4)y$ simplifies to $y$ because $(4)/(4)$ is equal to $1$ . So we rewrite the equation as: $\newline$ $y = (2)/(9)y + 7$
Move y terms: Now, we need to get all the y terms on one side. We can subtract $(\frac{2}{9})y$ from both sides to move it to the left side: $\newline$ $y - (\frac{2}{9})y = 7$
Find common denominator: To combine the $y$ terms, we need a common denominator. Since the denominators are $1$ and $9$ , the common denominator is $9$ . We can rewrite $y$ as $\frac{9}{9}y$ : $\frac{9}{9}y - \frac{2}{9}y = 7$
Combine $y$ terms: Now we can subtract the fractions: $\newline$ $\frac{9}{9}y - \frac{2}{9}y = \frac{7}{9}y$ $\newline$ So we have: $\newline$ $\frac{7}{9}y = 7$
Divide by $(7/9)$ : To solve for $y$ , we can divide both sides by $(7)/(9)$ : $\newline$ $y = \frac{7}{\left(\frac{7}{9}\right)}$
Multiply by reciprocal: To divide by a fraction, we multiply by its reciprocal. The reciprocal of $(\frac{7}{9})$ is $(\frac{9}{7})$ : $y = 7 \times \frac{9}{7}$
Simplify solution: Now we can simplify the right side by canceling out the $7$ s: $\newline$ $y = 9$