Write Equation: Write down the original equation. y/2 - 1/5 = 2 - y/3Find Common Denominator: Find a common denominator for the fractions to combine them effectively. The common denominator for 2, 5, and 3 is 30. Multiply each term by 30 to eliminate the denominators. 30(y/2) - 30(1/5) = 30(2) - 30(y/3)Multiply by Common Denominator: Simplify each term. 15y - 6 = 60 - 10ySimplify Terms: Move all y terms to one side of the equation and constants to the other side. 15y + 10y = 60 + 6Move Terms: Combine like terms. 25y = 66Combine Like Terms: Divide both sides by 25 to solve for y. y = 66 / 25Solve for y: Simplify the fraction if possible. y = 2.64

Algebra 2

Factor sums and differences of cubes

Full solution

\frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3}

Write Equation: Write down the original equation. $\newline$ $\frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3}$
Find Common Denominator: Find a common denominator for the fractions to combine them effectively. The common denominator for $2$ , $5$ , and $3$ is $30$ . $\newline$ Multiply each term by $30$ to eliminate the denominators. $\newline$ $30(y/2) - 30(1/5) = 30(2) - 30(y/3)$
Multiply by Common Denominator: Simplify each term. $15y - 6 = 60 - 10y$
Simplify Terms: Move all $y$ terms to one side of the equation and constants to the other side. $15y + 10y = 60 + 6$
Move Terms: Combine like terms. $\newline$ $25y = 66$
Combine Like Terms: Divide both sides by $25$ to solve for $y$ . $\newline$ $y = \frac{66}{25}$
Solve for y: Simplify the fraction if possible. $\newline$ $y = 2.64$