Questions: Solve for y 5y/8 - 2 = 7y/12 Simplify your answer as much as possible.

Transcript text: Solve for $y$ \[ \frac{5 y}{8}-2=\frac{7 y}{12} \] Simplify your answer as much as possible.

Solution

Solution Steps

To solve the equation $\frac{5y}{8} - 2 = \frac{7y}{12}$, we need to eliminate the fractions by finding a common denominator. Once the fractions are cleared, we can isolate $y$ on one side of the equation and solve for it. Finally, simplify the solution if possible.

Step 1: Eliminate Fractions

To eliminate the fractions in the equation $\frac{5y}{8} - 2 = \frac{7y}{12}$, we find a common denominator, which is 24. Multiply every term by 24 to clear the fractions:

\[ 24 \left(\frac{5y}{8}\right) - 24 \times 2 = 24 \left(\frac{7y}{12}\right) \]

This simplifies to:

\[ 15y - 48 = 14y \]

Step 2: Isolate $y$

Subtract $14y$ from both sides to isolate $y$:

\[ 15y - 14y = 48 \]

This simplifies to:

\[ y = 48 \]