Half of a number is at most 5 units from 14 Half of a number n is at most 5 units from 14 means:
The difference between 14 and half of n is less than 5.
| 14 – n/2 | ≤5
Multiply both sides by 2
| 28 – n | ≤ 10
Two cases are possible:
28 – n ≤ 10
WHERE
– ( 28 – n ) ≤ 10
1.
28 – n ≤ 10
28 ≤ 10 + n
28 – 10 ≤ n
18 ≤ n
2.
– ( 28 – n ) ≤ 10
– 28 + n ≤ 10
n ≤ 10 + 28
n ≤ 38
The solution:
18 ≤ n ≤ 38 |1/2n – 14| ≤5
Half of n is 1/2*n or 1/2n, you have to subtract 14 from it and you put all that in absolute value signs. Then, since it says is at most 5, you know it can be 5 or less, which is indicated by ≤ 5. \abs{\frac{n}{2}-14}\le 5