Question

The equation 3(4y-2)= -30 is solved in several steps below. For each step, choose the reason that best justifies it.
12y-6= -30
12y-6+6= -30+6
12y= -24
12y -24
—— = ——-
12 12
Y= -2

Answer Bank: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, Simplifying, Distributive Property

Answer 1

Answer:

see below

Step-by-step explanation:

3(4y-2)= -30  

12y-6= -30  Distributive Property

12y-6+6= -30+6   Addition Property of Equality   (the 6 on each side)

12y= -24    Simplifying  

12y -24

—— = ——-           Division Property of Equality    (divide by 12 on each side)      

12          12

Y= -2                Simplifying,  

Answer 2

The required reasons are Distributive Property, Addition Property of Equality, Simplifying, Division Property of Equality, Simplifying respectively.

Given:

The given equation is:

$3(4y-2)=-30$  

Several steps of solving the above equation are given.

To find:

The reasons for each step.

Explanation:

We have,

$3(4y-2)=-30$  

Using distributive property, we get

$3(4y)+3(-2)=-30$  

$12y-6=-30$

Add 6 on both sides.

$12y-6+6=-30+6$

$12y=-24$

Divide both sides by 12.

$\dfrac{12y}{12}=\dfrac{-24}{12}$

$y=-2$

Therefore the steps and reasons are shown below:

Steps                                     Reasons

$12y-6=-30$                        Distributive Property

$12y-6+6=-30+6$             Addition Property of Equality

$12y=-24$                             Simplifying

$\dfrac{12y}{12}=\dfrac{-24}{12}$                            Division Property of Equality

$y=-2$                                  Simplifying

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