I am thinking of a number. I multiply it by 2 and add 22. I get the same answer if I multiply by 4 and subtract 10. What is my number?

Remember you can do anything to an equaton as long as you do it to boht sides

so represent the number as n

n times 2 and add 22

2n+22

I get the same result when I multipily n by 4 and subtract 10

2n+22=4n-10

now solve

2n+22=4n-10

we can divide everybody by 2

n+11=2n-5

isolate the placeholder

subtract n from both sides

11=n-5

add 5 to both sides

16=n

The number times 2 plus 22 is 2n+22. The number times 4 minus 10 is 4n-10. This means the equation is 2n+22=4n-10. You need to balance this to get n. To do this get rid of some numbers. First minus 2n from each side. You are left with 22=2n-10. Then add 10 to both sides to get rid of it. You now have 2n=22. Finally, you need to get rid of the 2 in front of the n. 2n means 2xn so to get rid of it you need to divide both sides by 2. You are left with n=11 so your number is 11.