Solve the inequality. Graph and check your solutions.

Question

Solve the inequality. Graph and check your solutions.
yminus9greater thanminus11
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Part 1
ygreater than
  
enter your response here ​(Simplify your​ answer.)

GPT-4o mini · Answer

To solve the inequality $ y - 9 > -11 $, follow these steps: 1. **Add 9 to both sides**: $$ y - 9 + 9 > -11 + 9 $$ 2. **Simplify**: $$ y > -2 $$ So, the solution to the inequality is: $$ y > -2 $$ ### Graphing the Solution To graph $ y > -2 $: 1. Draw a number line. 2. Mark the point at $-2$. 3. Since this is a strict inequality (indicated by the greater than sign, not greater than or equal), draw an open circle at $-2$. 4. Shade the region to the right of $-2$ to indicate that $y$ can take any value larger than $-2$. ### Checking Solutions To check if the solution is correct, you can test a number greater than $-2$ and a number less than or equal to $-2$. - **Test $y = 0$** (which is greater than $-2$): $$ 0 - 9 > -11 \quad \Rightarrow \quad -9 > -11 \quad \text{(True)} $$ - **Test $y = -2$** (which is equal to $-2$): $$ -2 - 9 > -11 \quad \Rightarrow \quad -11 > -11 \quad \text{(False, since this is not greater than)} $$ - **Test $y = -3$** (which is less than $-2$): $$ -3 - 9 > -11 \quad \Rightarrow \quad -12 > -11 \quad \text{(False)} $$ These checks confirm the solution $y > -2$ is correct. ### Final Answer $$ y > -2 $$