Question

1. (01.02 hc)

the incorrect work of a student to solve an equation ( 2(y + 6)=4y ) is shown below:
step 1: ( 2(y + 6)=4y )
step 2: ( 2y + 8 = 4y )
step 3: ( 2y = 8 )
step 4: ( y = 4 )
which of the following explains how to correct step 2 and shows the correct value of ( y )? (5 points)
( 2 ) should be distributed as ( 2y + 12 ); ( y = 6 ).
( 2 ) should be distributed as ( 2y + 12 ); ( y = 3 ).
the equation should be ( y + 6 = 4y ) after division by ( 2 ); ( y = 2 ).
the equation should be ( y + 6 = 4y ) after division by ( 2 ); ( y = 1 ).

Explanation:

Step1: Identify the error in Step2

The student incorrectly calculated $2(y+6)$ as $2y+8$ instead of using proper distribution. The correct distribution is $2(y+6)=2y+12$, so the equation becomes $2y+12=4y$.

Step2: Isolate the variable terms

Subtract $2y$ from both sides to group like terms.
$2y+12-2y=4y-2y$
$12=2y$

Step3: Solve for y

Divide both sides by 2 to find the value of y.
$\frac{12}{2}=\frac{2y}{2}$
$y=6$

Answer:

2 should be distributed as $2y + 12$; $y = 6$.