How do you solve and graph $6 < - 2 m < 10$ $6<-2m<10$ ?

Question

2098 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-19T17:14:20

See process below

Given $6 < - 2 m < 10$ $6<-2m<10$

Take the left side $6 < - 2 m$ $6<-2m$

Multiply by -1 in both sides. The symbol "<" changes

$- 6 > 2 m$ $-6>2m$ . Now divide by 2 both sides and you get $- \frac{6}{2} > m$ $-6/2>m$ or equivalent $m < - 3$ $m<-3$

Take now the rigth side $- 2 m < 10$ $-2m<10$ . Apply the same process

$2 m > - 10$ $2m> -10$ or equivalent $m > - \frac{10}{2} = - 5$ $m> -10/2=-5$

In summary, we have two restrictions
$- 5 < m < - 3$ $-5 < m < -3$

This is equivalent to interval $(- 5, - 3)$ $(-5,-3)$ grafically is the segment between -5 and -3 but without both endpoints

How do you solve and graph 6<-2m<106<−2m<106<-2m<10?