# How do you solve - 7< 5 - 2y <= 1?

Jun 25, 2018

Shown below

#### Explanation:

Treat it like a normal linear equation question:

$- 7 < 5 - 2 y \le 1$

Get rid of the $5$ in the middle by -5 on each of the terms

$- 7 \textcolor{red}{\text{ "-5 ) < 5 -2y color(red)(" "-5) <= 1color(red)( " } - 5}$

$\implies - 12 < - 2 y \le - 4$

Divide each term by -2 to isolate $y$

When you divide by a negative number, the inequalities swap

$\implies 6 > y \ge 2$

$\implies \textcolor{b l u e}{2 \le y < 6}$

Jun 25, 2018

$y \in \left[2 , 6\right)$

#### Explanation:

we have
$- 7 < 5 - 2 y \le 1$
subtracting 5 on both sides
$- 12 < - 2 y \le - 4$
dividing 2 both sides
$- 6 < - y \le - 2$
multiplying -1 both sides
$6 > y \ge 2$
we get a range of y such that greater than equal to 2 and less than 6 also
hence $y \in \left[2 , 6\right)$