−2(7+y)≥−8(y+1)

We are given: ${\displaystyle -2(7+y)\ge -8(y+1)}$
Divide both sides by —2. Recall that when we multiply or divide both sides of an inequality by a negative number, we change the direction of the inequality:
${\displaystyle (7+y)\le 4(y+1)}$
Apply distributive property:
${\displaystyle 7+y\le 4y+4}$
Subtract 4 from both sides:
${\displaystyle 3+y\le 4y}$
Subtract y from both sides:
3<3y
Divide both sides by 3:
${\displaystyle 1\le y}$
or
${\displaystyle y\Rightarrow 1}$