`15(y-4)-2(y-9)+5(y+6)=0`

Options

A. `2/3`
B. `4/3`
C. `5/3`
D. `7/3`

Answer

To solve the equation \( 15(y-4) - 2(y-9) + 5(y+6) = 0 \), we will follow these steps:

### Step 1: Distribute the terms
We start by distributing the constants across the brackets.

\[ 15(y-4) = 15y - 60 \]
\[ -2(y-9) = -2y + 18 \]
\[ 5(y+6) = 5y + 30 \]

### Step 2: Substitute back into the equation
Now we substitute these expanded forms back into the equation:

\[ 15y - 60 - 2y + 18 + 5y + 30 = 0 \]

### Step 3: Combine like terms
Next, we combine all the \(y\) terms and the constant terms.

\[ (15y - 2y + 5y) + (-60 + 18 + 30) = 0 \]
\[ (15 - 2 + 5)y + (-60 + 18 + 30) = 0 \]
\[ 18y - 12 = 0 \]

### Step 4: Isolate \(y\)
Now we isolate \(y\) by adding 12 to both sides:

\[ 18y = 12 \]

### Step 5: Solve for \(y\)
Finally, we divide both sides by 18:

\[ y = \frac{12}{18} \]
\[ y = \frac{2}{3} \]

### Final Answer
The solution to the equation \( 15(y-4) - 2(y-9) + 5(y+6) = 0 \) is:

\[ y = \frac{2}{3} \]

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