Question

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

$12\cdot n=12\cdot 6$

Short answer

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

Step-by-step solution

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.