How do you solve 4<=x+1<8?

Apr 15, 2018

The solution is $3 \le x < 7$.

Explanation:

You can subtract $1$ from all of the "sides", just like you would in a regular inequality:

$4 \textcolor{w h i t e}{\textcolor{w h i t e}{-} 1} \le x + 1 \textcolor{w h i t e}{\textcolor{w h i t e}{-} 1} < 8 \textcolor{w h i t e}{\textcolor{w h i t e}{-} 1}$

$4 \textcolor{b l u e}{-} \textcolor{b l u e}{1} \le x + 1 \textcolor{b l u e}{-} \textcolor{b l u e}{1} < 8 \textcolor{b l u e}{-} \textcolor{b l u e}{1}$

$4 \textcolor{b l u e}{-} \textcolor{b l u e}{1} \le x \textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l a c k}{+} 1 \textcolor{b l u e}{-} \textcolor{b l u e}{1}}}} < 8 \textcolor{b l u e}{-} \textcolor{b l u e}{1}$

$4 \textcolor{b l u e}{-} \textcolor{b l u e}{1} \le x \textcolor{w h i t e}{\textcolor{w h i t e}{+} 1 - 1} < 8 \textcolor{b l u e}{-} \textcolor{b l u e}{1}$

$3 \textcolor{w h i t e}{\textcolor{w h i t e}{-} 1} \le x \textcolor{w h i t e}{\textcolor{w h i t e}{+} 1 - 1} < 8 \textcolor{b l u e}{-} \textcolor{b l u e}{1}$

$3 \textcolor{w h i t e}{\textcolor{w h i t e}{-} 1} \le x \textcolor{w h i t e}{\textcolor{w h i t e}{+} 1 - 1} < 7$

That's the solution set. Hope this helped!