Q62. - Algebra 1

Question

Find the value of $n$. Then name the property used in each step. (Lesson 1-3)

$12\cdot n=12\cdot 6$

Step-by-Step Solution

Answer

The value of $n$ is $6$. The main properties used are the multiplicative property of zero and the distributive property.

Step 1. State the property.

The multiplicative property of zero states that for any number $a$, the product of $a$ and $0$ is $0$.

So, $a\cdot 0=0$.

 

The distributive property states that multiplication is distributive over addition or subtraction.

So, $a\left(b\pm c\right)=ab\pm ac$.

Step 2. Write the given equation.

The given equation is $12\cdot n=12\cdot 6$.

Step 3. Solve the given equation.

$12\cdot n=12\cdot 6$  (Given equation)

 

$12\cdot n-12\cdot 6=12\cdot 6-12\cdot 6$  (Subtract $12\cdot 6$ from both sides)

 

$12\cdot n-12\cdot 6=0$  (Simplify)

 

$12\cdot \left(n-6\right)=0$  (Distributive property)

 

$n-6=0$  (Multiplicative property of zero)

 

$n-6+6=0+6$  (Add 6 to both sides)

 

$n=6$  (Simplify)

 

So, the solution of the given equation is $n=6$ and the main properties used are the multiplicative property of zero and the distributive property.