Twice the opposite of a number is increased by 5 and this sum is multiplied by 2. the result is 22 greater than the number. what is the number?

Okay so lets look at what it says.

Opposite in the case of math almost always means negative.  So (2(-n)+5)*2.  This can be simplified to (-2n+5)*2 = 22 + n

Again, simplify it and its -4n+10 = 22 + n

Subtract 10 from both sides and its -4n = 12 + n

Add 4n to both sides and you get 0 = 12 + 5n

Subtract 12 from both sides and its 5n = -12.

Divided both sides by five and you have n = -12/5