When 6 times a number is subtracted from 12, the result is 4 times the difference of 5 and the number. What is the equation?

Question

This is a question on homework i need help on.

Answer 1

12 - 6n = 4(5 - n) 

12 - 6n = 20 - 4n 
- 6n + 4n = 20 - 12 
- 2n = 8 
n = - 4 

Answer 2

12 - 6x = 4(x - 5)

 

 

Answer 3

Hi Eileen;

12-6x=4(5-x)

12-6x=20-4x

Let's add 6x to both sides...

12-6x+6x=20-4x+6x

12=20+2x

Let's subtract 20 from both sides...

12-20=2x

-8=2x

Let's divide both sides by 2...

-8/2=2x/2

-4=x

Let's check our work...

12-6x=4(5-x)

12-[6(-4)]=4(5--4)

Subtracting a negative number is the same thing as adding...

12-(-24)=4(5+4)

12+24=4(9)

36=36

 

You use the phrase "the difference of 5 and the number."

It could be "the difference of the number and 5."

12-6x=4(x-5)

12-6x=4x-20

Let's add 6x to both sides as we proceed to isolate x...

6x+12-6x=4x-20+6x

12=10x-20

Let's add 20 to both sides...

12+20=10x-20+20

32=10x

Let's divide both sides by 10...

32/10=(10x)/10

3.2=x

 

Let's check our work...

12-6x=4(x-5)

12-[6(3.2)]=4(3.2-5)

12-19.2=4(-1.8)

-7.2=-7.2