Question

How do you solve `|-4x + 10| ≤ 46`?

Answer 1

The solution is
For all values above 9 and less than or equal to 14, the relation is valid

Explanation:

`abs(-4x+10)<=46`
`-4x+10<=46`
`-4x<=46-10`
`-4x<=36`
`-x<=36/4`
`-x<=9`
`x>9`
or
`-4x+10<=-46`
`-4x<=-46-10`
`-4x<=-56`
`4x<=56`
`x<=56/4`
`x<=14`
The solution is
`x>9,x<=14`
For all values above 9 and less than or equal to 14, the relation is valid

Answer 2

The solution is `x in [-9,14]`

Explanation:

The inequality is

`|-4x+10|<=46`

The solution is

`{(4x-10<=46),(-4x+10<=46):}`

`<=>`, `{(4x<=46+10),(4x>=10-46):}`

`<=>`, `{(4x<=56),(4x>=-36):}`

`<=>`, `{(x<=56/4),(x>=-36/4):}`

`<=>`, `{(x<=14),(x>=-9):}`

The solution is

`x in [-9,14]`

graph{|4x-10|-46 [-105.4, 105.4, -52.7, 52.7]}