Half of a number n is at most 5 units from 14 means:
Difference between 14 and half times n is less than 5.
| 14 - n / 2 | ≤ 5
Multiply both sides by 2
| 28 - n | ≤ 10
Two cases are possible:
28 - n ≤ 10
OR
- ( 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
Solution:
18 ≤ n ≤ 38
Half of a number is at most 5 inits from 14
3 answers
|1/2n - 14| ≤ 5
Half of n is 1/2 * n or 1/2n, you need to subtract 14 from that and you put all of it in absolute value signs. Then, since it says is at most 5, you know it can be 5 or less which is shown by ≤ 5.
Half of n is 1/2 * n or 1/2n, you need to subtract 14 from that and you put all of it in absolute value signs. Then, since it says is at most 5, you know it can be 5 or less which is shown by ≤ 5.
\abs{\frac{n}{2}-14}\le 5