Questions: 4(4y-3)-(y-5)=-52

Solution Steps

To solve the equation \(4(4y - 3) - (y - 5) = -52\), we need to follow these steps:

1. Distribute the constants inside the parentheses.
2. Combine like terms.
3. Isolate the variable \(y\) by performing algebraic operations.

First, distribute the constants inside the parentheses: \[ 4(4y - 3) - (y - 5) = -52 \] \[ 16y - 12 - y + 5 = -52 \]

Combine the like terms on the left-hand side: \[ (16y - y) + (-12 + 5) = -52 \] \[ 15y - 7 = -52 \]

Add 7 to both sides of the equation to isolate the term with \( y \): \[ 15y - 7 + 7 = -52 + 7 \] \[ 15y = -45 \]

Divide both sides by 15 to solve for \( y \): \[ y = \frac{-45}{15} \] \[ y = -3 \]

Final Answer