Questions: Solve for y and graph the solution. y-3+y>13 or y+18-5y>18

Transcript text: Solve for $y$ and graph the solution. \[ y-3+y>13 \text { or } y+18-5 y>18 \]

Solution

Solution Steps

Step 1: Solve the first inequality

We have $y - 3 + y > 13$. Combining like terms gives $2y - 3 > 13$. Adding 3 to both sides gives $2y > 16$. Dividing both sides by 2 gives $y > 8$.

Step 2: Solve the second inequality

We have $y + 18 - 5y > 18$. Combining like terms gives $-4y + 18 > 18$. Subtracting 18 from both sides gives $-4y > 0$. Dividing both sides by -4 and flipping the inequality sign gives $y < 0$.

Step 3: Combine the inequalities

We have $y > 8$ or $y < 0$.

Step 4: Graph the solution

The solution is $y > 8$ or $y < 0$. On the number line, we have an open circle at 0 and an arrow pointing to the left, representing $y < 0$. We also have an open circle at 8 and an arrow pointing to the right, representing $y > 8$.

Final Answer

The solution is $ \boxed{y < 0 \text{ or } y > 8} $. The graph includes an open circle at 0 and an arrow to the left, and an open circle at 8 and an arrow to the right.

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