SOLUTION: Please help me solve this problem The product of 6 and 9 times the number is the same as the difference of 10 times the number and 2

Click here to see ALL problems on Equations

Question 103022: Please help me solve this problem
The product of 6 and 9 times the number is the same as the difference of 10 times the number and 2
Answer by doukungfoo(195) (Show Source):
You can put this solution on YOUR website!
lets call the number x
Now we have to turn this sentence into an equation
The product of 6 and 9 times the number is the same as the difference of 10 times the number and 2
We will break it down piece by piece
first we are told the product of 6 and 9
by definition product is:
The number or quantity obtained by multiplying two or more numbers together.
so the product of 6 and 9 is 54
next part of the sentence tells us that
times the number
so 54 times x
or
54x
So far we have transformed the first part of the senctence
"The product of 6 and 9 times the number"
into
54x
The next word in the sentence is "is"
When you see the word "is"
this lets you know you need an equal sign
so now we have
54x=
The remaining part of the sentence will tell us what 54x equals
so lets look at what comes after the "is"
the same as the difference of 10 times the number and 2
the word "difference" means we are going to subtract something
so what are we going to subtract?
look at the last part of the sentence
"10 times the number and 2"
ok so 10 times the number. "times" tells us to multiply
so we get 10x
remember the number is x
so 10 times the number is 10x
Ok so we have 10x and we are going to subtract something from it
what are we going to subtract?
2
so now we have
10x - 2
put this together with the first part of the sentence and we get a complete equation
54x = 10x - 2
Now we are ready to solve for x
54x = 10x - 2
first move 10x over to the right
to do this subtract 10x from both sides
54x - 10x = 10x - 10x -2
the 10x's on the right side cancel out which leaves
54x - 10x = -2
combine like terms
44x = -2
solve for x by dividing both sides by 44
44x/44 = -2/44

this fraction can be reduced so the final answer is

Check the answer by replacing x in the orginal equation with

Thats it.