Question

Which number line represents the solution set for the given inequality x + 1 < (or equal to) -3 OR -4x < -8

Answer 1

we are given inequalities as

`x+1\leq -3`

Subtract both sides by 1

`x+1-1\leq -3-1`

`x\leq -4`

so, we get interval as

`(-\infty,-4]`

we have

`-4x<-8`

we can divide both sides by -4

`(-4x)/(-4) >(-8)/(-4)`

`x >2`

so, we get interval as

`(2,\infty)`

now, we can combine them

`(-\infty,-4]`∪
`(2,\infty)`

now, we can draw number line and locate this interval

we get