$$ 19 x+5\end{array} $$

Question

$$ 1<\quad \begin{array}{c}	ext { Solve for } x 	ext { and graph your solution. } \ 2 x-9>9 x+5\end{array} $$

UpStudy AI · Accepted Answer

To solve the inequality $$2x - 9 > 9x + 5$$ and graph the solution, follow these steps: ### **Step 1: Solve the Inequality** 1. **Start with the original inequality:** $$ 2x - 9 > 9x + 5 $$ 2. **Subtract $$2x$$ from both sides to get all $$x$$-terms on one side:** $$ -9 > 7x + 5 $$ 3. **Subtract $$5$$ from both sides to isolate the term with $$x$$:** $$ -14 > 7x $$ 4. **Divide both sides by $$7$$ to solve for $$x$$:** $$ -2 > x $$ This can also be written as: $$ x < -2 $$ ### **Step 2: Graph the Solution on a Number Line** 1. **Draw a horizontal number line.** 2. **Mark the boundary point at $$x = -2$$ with an open circle** (since the inequality is strict $$<$$, meaning $$x = -2$$ is not included). 3. **Shade the region to the left of $$x = -2$$** to represent all real numbers less than $$-2$$. #### **Graphical Representation:** ``` <---|-----|-----|-----|-----|-----|--> -4 -3 -2 -1 0 1 ○----------------> ``` - The open circle at $$-2$$ indicates that $$-2$$ is not included in the solution. - The arrow to the left shows that all numbers less than $$-2$$ satisfy the inequality. ### **Final Answer** All real numbers less than –2 satisfy the inequality. **Solution:** $$x < -2$$ **Graph:** ![Number line showing an open circle at -2 and shading to the left](https://i.imgur.com/D1oX9IA.png) All real numbers less than –2 satisfy the inequality. **Solution:** $$x < -2$$ **Graph:** ``` <---|-----|-----|-----|-----|-----|--> -4 -3 -2 -1 0 1 ○----------------> ``` - The open circle at $$-2$$ indicates that $$-2$$ is not included. - The arrow to the left shows all numbers less than $$-2$$ are part of the solution.

Upstudy AI Solution

Answer

Solution

Step 1: Solve the Inequality

Step 2: Graph the Solution on a Number Line

Graphical Representation:

Final Answer

The Deep Dive

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