Question

Half of a number is at most 5 inits from 14

Answer 1

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

Answer 2

|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.

Answer 3

\abs{\frac{n}{2}-14}\le 5