Question

solve the compound inequality.
2y + 6 < 8 and 3y + 3 < 18
graph the solution on the number line.
if there is no solution, click on
o solution\.

Explanation:

Step1: Solve first inequality

Subtract 6 from both sides:
$2y + 6 - 6 < 8 - 6$
$2y < 2$
Divide by 2:
$\frac{2y}{2} < \frac{2}{2}$
$y < 1$

Step2: Solve second inequality

Subtract 3 from both sides:
$3y + 3 - 3 < 18 - 3$
$3y < 15$
Divide by 3:
$\frac{3y}{3} < \frac{15}{3}$
$y < 5$

Step3: Find intersection of solutions

Since we have "and", we take the overlap of $y < 1$ and $y < 5$, which is $y < 1$.

Answer:

The solution to the compound inequality is $y < 1$. To graph this:

• Place an open circle at $1$ on the number line
• Draw an arrow pointing left from the open circle to represent all values less than 1.