How do you solve the compound inequality $2w+1<-9$ and $4w+2<10$ ?

Question

1296 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-26T09:56:42

$w < -5$

There is one variable $(w)$

Solve each inequality separately.

$2w+1 < -9$

$2w < -9-1$

$2w < -10$

$w < -5$

and

$4w +2 < 10$

$4w < 10 -2$

$4w < 8$

$w < 2$

We have 2 answers for $w$ , but the final answer must be a solution for BOTH inequalities.

Values from -5 to 2 will only be true for the second inequality, but not for the first, they are therefore not valid.

The solution $w<-5$ includes the solution $w <2$

How do you solve the compound inequality 2w+1<-92w+1<-9 and 4w+2<104w+2<10?