Question

Half of a number n is at most 5 units from 14

(Write the absolute value inequality)

Answer 1

Answer: 18≤n≤38 is absolute value inequality for the problem.

Explanation:

Given situation:- Half of a number n is at most 5 units from 14

that means the difference between 14 and half times n is less than 5

`\Rightarrow |14-(1)/(2) * n|\leq 5\\\Rightarrow|2( 14-(1)/(2) * n)|\leq2(5)\\\Rightarrow|2(14)-2((1)/(2) * n)|\leq2(5)\ \text{(Multiplying 5 on the both sides)}\\\Rightarrow|\ 28-n|\leq10\\\Rightarrow\ 28-n\leq10\ or\ -(28-n)\leq10\\\Rightarrow\ n=28-10=18\ or\ n=28+10=38\\(i.e.)\ 18\leq\ n\leq \ 38`

⇒18≤n≤38 is absolute value inequality for the problem.