# How do you solve and write the following in interval

How do you solve and write the following in interval notation: $4\le 3-x<8$ ?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Jayvion Mclaughlin
Step 1
Isolate x in the middle interval by subtracting 3 from all 3 intervals
$4-3\le 3-3-x<8-3$
$⇒1\le -x<5$
multiply all 3 intervals by - 1 remembering to reverse the inequality signs
$⇒-1\ge x>-5←\phantom{\rule{1ex}{0ex}}\text{reverse signs}$
in interval notation as $\text{in interval notation as}\phantom{\rule{1ex}{0ex}}\left(-5,-1\right]$