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

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. \[ y-3+y>13 \text { or } y+18-5 y>18 \]
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Solution

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Solution Steps

Step 1: Solve the first inequality

We have y3+y>13y - 3 + y > 13. Combining like terms gives 2y3>132y - 3 > 13. Adding 3 to both sides gives 2y>162y > 16. Dividing both sides by 2 gives y>8y > 8.

Step 2: Solve the second inequality

We have y+185y>18y + 18 - 5y > 18. Combining like terms gives 4y+18>18-4y + 18 > 18. Subtracting 18 from both sides gives 4y>0-4y > 0. Dividing both sides by -4 and flipping the inequality sign gives y<0y < 0.

Step 3: Combine the inequalities

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

Step 4: Graph the solution

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

Final Answer

The solution is y<0 or y>8 \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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