Question

Solve the following inequation, write the solution set and represent it on the real number line.

`2x − 5/3 < "3x"/5 + 10 ≤ "4x"/5 + 11; x ∈ R`

Answer 1

Given the inequality:

`2x − 5/3 < "3x"/5 + 10 ≤ "4x"/5 + 11; x ∈ R`

Solving the first,

`2x − 5/3 < "3x"/5 + 10`

2x − `5/3 < (3x)/5 + 10`

`"7x"/5 < 35/3`

`x < 325​`

Now solving the second part,

`(3x)/5 ​+ 10 ≤ 54 x ​+ 11`

`10 − 11 ≤ "4x"/5 + 11`

−5 ≤ x

Hence, the solution set is:

{−5 ≤  x < `25/3`, x ∈ R}