How do I solve the following equation :  4(2y+1)=2(12-y)I know the answer is y=2 but i do not know how to work it out

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You have to solve the equation 4(2y+1) = 2(12-y).

First let's start with 4(2y+1) = 2(12-y)

open the brackets

=> 4*2y + 4*1 = 2*12 - 2*y

=> 8y + 4 = 24 - 2y

now move the terms with y to one side, and the numeric terms to the other side. Remember that when you move a term to the other side of the equation, its sign changes

=> 8y + 2y = 24 - 4

=> 10y = 20

divide both the sides by 10

=> y = 20/10 = 2.

That's how you get y = 2. Hope it's clear now.

carlatullis's profile pic

carlatullis | Elementary School Teacher | eNotes Newbie

Posted on

First multiply:  (4 x 2y) + (4 x 1) = (2 x 12) - (2 x y) =                       8y + 4 = 24 - 2y    

Now, add 2y to both sides:  8y + 2y + 4 = 24 - 2y + 2y = 10y + 4 = 24

Now, subtract 4 from both sides:  10y + 4 - 4 = 24 - 4 = 10y = 20

Now, divide both sides by 10:  10y/10 = 20/10

Your answer:  y = 2

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve the equation 4(2y+1)=2(12-y).

This is a linear equation of one variable y. So we add or subtract equals , multiply or divide by equals (but no multiplication or division by zero!) until we redice the equation to y = some number.

We divide both sides of 4(2y+1)=2(12-y)by 2:

2(2y+1) = 12-y.

2*2y+2*1 = 12-y.

4y+2 = 12-y.

Add y to both sides:

4y+2+y = 12.

5y+2 = 12.

Subtract 2 from both sides:

5y = 12-2 = 10.

5y/5 = 10/5 = 2.

y = 2.

So y = 2 is the solution.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll apply the distributive property of multiplication, over addition:

4(2y+1)=2(12-y)

4*2y + 4*1 = 2*12 - 2*y

8y + 4 = 24 - 2y

We'll isolate y to the left side. For this reason, we'll add 2y both sides and subtract 4 both sides:

8y + 2y = 24 - 4

We'll combine like terms:

10y = 20

We'll divide by 10:

y = 2

This is one way to solve the given equation.

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