Questions: Solve for (y). [ -4(-4 y+9)-y=7(y-6)-4 ] Simplify your answer as much as possible. [ y= ]

Solve for (y). [ -4(-4 y+9)-y=7(y-6)-4 ] Simplify your answer as much as possible. [ y= ]
Transcript text: Solve for $y$. \[ -4(-4 y+9)-y=7(y-6)-4 \] Simplify your answer as much as possible. \[ y= \]
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Solution

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Solution Steps

Step 1: Expand and Simplify the Equation

We start with the equation: \[ -4(-4y + 9) - y = 7(y - 6) - 4 \] Expanding both sides gives: \[ 16y - 36 - y = 7y - 42 - 4 \] This simplifies to: \[ 15y - 36 = 7y - 46 \]

Step 2: Collect Like Terms

Next, we rearrange the equation to collect all terms involving \( y \) on one side and constant terms on the other: \[ 15y - 7y = -46 + 36 \] This simplifies to: \[ 8y = -10 \]

Step 3: Solve for \( y \)

Now, we isolate \( y \) by dividing both sides by 8: \[ y = \frac{-10}{8} = \frac{-5}{4} \]

Final Answer

The solution for \( y \) is: \[ \boxed{y = -\frac{5}{4}} \]

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