How do I solve this problem?

Question

the difference of a number t and 7 is greater than 10 and less than 20

Answer 1

We can convert the given information into these two inequalities:

(1) t-7 > 10

(2) t-7 < 20

 

By adding 7 on both sides we get

(1) t > 17

(2) t < 27

 

So t must be greater than 17 and less than 27.

Answer 2

 

10<(t-7)<20

t-7>10 

t>10+7 (add 7 to both sides)

t>17

and

t-7<20

t<20+7 (add 7 to both sides)

t<27

Therefore, 17<t<27.

 

So the solutions for t would be t∈{18, 19, 20, 21, 22, 23, 24, 25, 26}.