Question

solve the compound inequality.
$4y + 5 < 25$ or $2y - 6 < -2$
write the solution in interval notation.
if there is no solution, enter $\varnothing$.

Explanation:

Step1: Solve first inequality

Subtract 5 from both sides:
$4y + 5 - 5 < 25 - 5$
$4y < 20$
Divide by 4:
$\frac{4y}{4} < \frac{20}{4}$
$y < 5$

Step2: Solve second inequality

Add 6 to both sides:
$2y - 6 + 6 < -2 + 6$
$2y < 4$
Divide by 2:
$\frac{2y}{2} < \frac{4}{2}$
$y < 2$

Step3: Combine solutions (OR)

Since "or" means all values satisfying either inequality, the solution is all $y < 5$ (as $y < 2$ is a subset of $y < 5$).

Answer:

$(-\infty, 5)$