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

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

Solution

Solution Steps

To solve the given linear equation, we need to eliminate the fractions by finding a common denominator. Then, we can simplify the equation by combining like terms and isolating the variable $ y $.

Step 1: Eliminate Fractions

To eliminate the fractions, we find a common denominator for the terms involving $ y $. The least common multiple of 12 and 8 is 24. Multiply every term by 24 to clear the fractions: \[ 24 \left(\frac{7y}{12}\right) - 24 \times 2 = 24 \left(\frac{5y}{8}\right) \] This simplifies to: \[ 14y - 48 = 15y \]

Step 2: Isolate the Variable

Rearrange the equation to isolate $ y $ on one side: \[ 14y - 15y = 48 \] Simplify the left side: \[ -y = 48 \]

Step 3: Solve for $ y $

Multiply both sides by -1 to solve for $ y $: \[ y = -48 \]