SOLUTION: Four times the difference of a number and 2 is the same as 2 increased by four times the number plus twice the number. Find the number. How do you solve this? I don't understand

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Question 214847: Four times the difference of a number and 2 is the same as 2 increased by four times the number plus twice the number. Find the number. How do you solve this? I don't understand it.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Four times the difference of a number and 2 is the same as 2 increased by four times the number plus twice the number. Find the number.

Step 1. Let n be the number.

Step 2. Let n-2 is the difference between the number and 2.

Step 3. Let 4(n-2) is four times the difference between the number and 2

Step 4. Let 2+4n+2n be 2 increased by 4 times the number plus twice the number

where 4n is four times the number and 2n is twice the number.

Step 5. Set expressions in Step 3 and 4 equal.

4%28n-2%29=2%2B4n%2B2n=2%2B6n

4n-8=2%2B6n

Subtract 4n to both sides of the equation

4n-8-4n=2%2B6n-4n

-8=2%2B2n

Subtract -2 to both sides of the equation to get solve for n

-8-2=2%2B2n-2

-10=2n

Divide by 5 to both sides of equation to get n

-10%2F2=2n%2F2

-5=n

n=-5

Step 6. ANSWER. The number is -5.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J