Question

What is the solution to the inequality?

-2/3 (2x - 1/2) ≤ 1/5x - 1

Express your answer in interval notation.

Answer 1

Alright, lets get started.

`-(2)/(3) (2x-(1)/(2) )\leq (1)/(5)x -1`

Distributing
`-(2)/(3)` into parenthesis

`-(4x)/(3)+ (2)/(6) \leq (x)/(5) -1`

`-(4x)/(3)+ (1)/(3) \leq (x)/(5) -1`

Subtracting
`(1)/(3)` from both sides

`-(4x)/(3)+ (1)/(3)- (1)/(3)\leq(x)/(5)-1- (1)/(3)`

`-(4x)/(3) \leq (x)/(5)- (4)/(3)`

Adding
`(4)/(3)` in both sides

`-(4x)/(3)+ (4)/(3) \leq (x)/(5) -(4)/(3)+ (4)/(3)`

`-(4x)/(3) +(4)/(3) \leq (x)/(5)`

Adding
`(4x)/(3)` in both sides

`-(4x)/(3) +(4)/(3) +(4x)/(3) \leq (x)/(5) +(4x)/(3)`

`(4)/(3) \leq (x)/(5) +(4x)/(3)`

Making common denominator, adding fractions

`(4)/(3) \leq (23x)/(15)`

It means

`23x\geq (4*15)/(3)`

`23x\geq 20`

Dividing 23 in both sides

`x\geq (20)/(23)`

In interval notation

[
`(20)/(23)`,∞)

This is the answer

Hope it will help :)