Solve the inequality and graph the solution.

Question

8<3(v–2)–4
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality $8<3(v-2)-4$, we first simplify the right-hand side:

1. Distribute the $3$: $$3(v-2)=3v-6$$ So the inequality becomes: $$8<3v-6-4$$

2. Combine like terms on the right: $$3v-6-4=3v-10$$ Therefore, the inequality is: $$8<3v-10$$

3. Add $10$ to both sides to isolate the term with $v$: $$8+10<3v$$ This simplifies to: $$18<3v$$

4. Divide both sides by $3$ to solve for $v$: $$\frac{18}{3}<v$$ Which simplifies to: $$6<v$$ or in standard form: $$v>6$$

Graphing the Solution

1. Plotting the endpoints: The solution is $v>6$. We’ll plot the point $6$.

2. Closed vs. Open endpoints: Since the inequality is strictly greater than (not including $6$), we make the endpoint $6$ open.

3. Graphing the ray: The graph will show all values of $v$ to the right of $6$:

   • Use an open circle at $6$ to indicate that $6$ is not included in the solution.
   • Shade the region to the right of $6$ to represent all numbers greater than $6$.

Final Result

The solution to the inequality is $v>6$, and the graph will look like this:

• An open circle at $6$.
• A line extending to the right (toward positive infinity).

$$\text{Graph:}$$ $$\text{(Open circle at 6, shading to the right)}$$