Question

solve the compound inequality. 2y + 3 ≤ 3 and - 3y > 15. graph the solution on the number - line. if there is no solution, click on
o solution\.

Explanation:

Step1: Solve the first - inequality

Solve \(2y + 3\leqslant3\). Subtract 3 from both sides: \(2y+3 - 3\leqslant3 - 3\), getting \(2y\leqslant0\). Then divide both sides by 2: \(y\leqslant0\).

Step2: Solve the second - inequality

Solve \(-3y>15\). Divide both sides by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So \(y < - 5\).

Step3: Find the intersection

The solution of the compound - inequality is the intersection of \(y\leqslant0\) and \(y < - 5\). The intersection is \(y < - 5\).

Answer:

On the number - line, we would mark an open circle at - 5 (because \(y\) is strictly less than - 5) and shade to the left of - 5.