Question

question 10 of 25 (1 point) | question attempt: 1 of unlimited
select
o solution\ if applicable.
part: 2 / 4
part 3 of 4
(b) $-\frac{2}{3}y < 8$ or $0.9 \leq 0.3y$
the solution set is

Explanation:

Step1: Solve the first - inequality

Multiply both sides of $-\frac{2}{3}y < 8$ by $-\frac{3}{2}$. When multiplying an inequality by a negative number, the direction of the inequality sign changes. So $y>8\times(-\frac{3}{2})$, which simplifies to $y > - 12$.

Step2: Solve the second - inequality

Divide both sides of $0.9\leq0.3y$ by $0.3$. We get $y\geq\frac{0.9}{0.3}$, which simplifies to $y\geq3$.

Step3: Find the union of the solution sets

The solution of the compound inequality $-\frac{2}{3}y < 8$ or $0.9\leq0.3y$ is the union of the solution sets of the two individual inequalities. Since $y > - 12$ and $y\geq3$, the union is $y>-12$. In interval notation, the solution set is $(-12,\infty)$.

Answer:

$(-12,\infty)$