Question

solve for y.
7 = 7(5 + 3y) - 19y
y =

Explanation:

Step1: Expand the right side

First, we expand \( 7(5 + 3y) \) using the distributive property \( a(b + c)=ab+ac \). So \( 7(5 + 3y)=7\times5 + 7\times3y = 35+21y \). The equation becomes \( 7=35 + 21y-19y \).

Step2: Combine like terms

Next, we combine the \( y \)-terms on the right side. \( 21y-19y = 2y \), so the equation is now \( 7=35 + 2y \).

Step3: Isolate the variable term

Subtract 35 from both sides to isolate the term with \( y \). \( 7-35=35 + 2y-35 \), which simplifies to \( - 28=2y \).

Step4: Solve for y

Divide both sides by 2 to solve for \( y \). \( \frac{-28}{2}=\frac{2y}{2} \), so \( y=-14 \).

Answer:

\( y = - 14 \)