`2|(2x)/3 + 1|>=4`

This gives

`|(2x)/3 + 1|>=2`

So either...

`(2x)/3+1<=-2`

OR

`(2x)/3+1>=2`

Multiply both sides by 3

`2x + 3 ≤ -6 `

`2x ≤ -9`

`x<=-9/2`

OR

`2x + 3 ≥ 6 `

`2x ≥ 3`

`x>=3/2`

Solution: `x<=-9/2 = -4.5,\ "or"\ x>=3/2=1.5`

Here's the graph of our solution:

12340-1-2-3-4-5-6x-4.51.5Open image in a new page

Please support IntMath!