Question

analyze the worked example. then, solve each equation for y.
1 ( 7 = y + 3(y + 2) )
use the distributive property to rewrite the right side of the equation
( 7 = y + square y + square )
combine like terms to rewrite the equation in two - step form.
( 7 = square y + square )
follow steps to isolate the variable.
(also some other equations like (-2x + 4 + 5x=-11), ((-2x + 5x)+4=-11), (3x + 4=-11) are partially visible)

Explanation:

Step1: Apply Distributive Property

The equation is \(7 = y + 3(y + 2)\). Using the distributive property \(a(b + c)=ab+ac\), we get \(7 = y + 3y+3\times2\), which simplifies to \(7 = y + 3y + 6\).

Step2: Combine Like Terms

Combine the \(y\) terms: \(y+3y = 4y\), so the equation becomes \(7 = 4y+6\).

Step3: Subtract 6 from Both Sides

Subtract 6 from both sides: \(7 - 6=4y + 6-6\), which gives \(1 = 4y\).

Step4: Divide by 4

Divide both sides by 4: \(\frac{1}{4}=y\) or \(y=\frac{1}{4}\).

Answer:

\(y = \frac{1}{4}\)