Questions: Solve the equation for (y). [ 0.12(y-9)+0.14 y=0.02 y-2.7 ] (y=) □ (Type an integer or a decimal.)

Solution Steps

To solve the equation for \( y \), we need to follow these steps:

1. Distribute the 0.12 through the parentheses.
2. Combine like terms on both sides of the equation.
3. Isolate the variable \( y \) by moving all terms involving \( y \) to one side and constants to the other.
4. Solve for \( y \).

First, we distribute \(0.12\) through the parentheses in the equation: \[ 0.12(y - 9) + 0.14y = 0.02y - 2.7 \] \[ 0.12y - 1.08 + 0.14y = 0.02y - 2.7 \]

Next, we combine the like terms on the left side of the equation: \[ (0.12y + 0.14y) - 1.08 = 0.02y - 2.7 \] \[ 0.26y - 1.08 = 0.02y - 2.7 \]

We move all terms involving \( y \) to one side and constants to the other side: \[ 0.26y - 0.02y = -2.7 + 1.08 \] \[ 0.24y = -1.62 \]

Finally, we solve for \( y \) by dividing both sides by \( 0.24 \): \[ y = \frac{-1.62}{0.24} \] \[ y = -6.75 \]

Final Answer