Question

3(x-1)≤ ½(x+1) -6. Topic is Linear inequalities ​

Answer 1

`x\le \:-1`

Explanation:

`3\left(x-1\right)\le (1)/(2)\left(x+1\right)-6`

`3x-3\le \:-(11)/(2)+(1)/(2)x`

`3x\le \:-(5)/(2)+(1)/(2)x\\`

`(5)/(2)x\le \:-(5)/(2)`

`5x\le \:-5`

`x\le \:-1`

x = -1

3(-2) ≤ ½(0) - 6

-6 ≤ 0 - 6

-6 ≤ -6

This is true.

x = -2

3(-3) ≤ ½(-1) - 6

-9 ≤ -½ - 6

-9 ≤
`-(13)/(2)`

This is also true.

Therefore, x ≤ -1.