Answer
$y\ \ \leq\ \ 1$
Work Step by Step
Applying the properties of inequality, we can
P1. add any number to both sides,
P2. multiply (or divide) both sides with a positive
$\quad $ number to arrive at a valid inequality.
$\quad $ If we
P3. multiply multiply (or divide) both sides with a negative number,
we must change the direction of the inequality sign, to arrive at a valid inequality..
Our goal is to, step by step, isolate the unknown on one side and interpret the result
(which, if any, will be an interval)
-----------------------------
$-2(3y-8)\geq 5(4y-2)$
...expand parentheses
$-6y+16\geq 20y-10\qquad \qquad $P1: ...$/-16$
$-6y\geq 20y-26\qquad \qquad $P1: ...$/-20y$
$-26y\geq-26 \qquad\qquad $P$3$: ...$/\div(-9)$... (negative)
$y\ \ \leq\ \ 1$
In interval notation:$\qquad (-\infty, 1]$.
