Other than a no solution​ set, use interval notation to express the solution set and then graph the solution set on a number line.
3 left parenthesis x plus 1 right parenthesis plus 4 greater than or equals 2 x plus 10

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution is 
  
enter your response here. ​(Type the solution using interval​ notation.)
B.
The solution set is empty set.

To solve the inequality:

\[
3(x + 1) + 4 \geq 2x + 10
\]

we first need to simplify and solve for \( x \).

### Step-by-Step Solution

1. **Expand and simplify the inequality:**

\[
3(x + 1) + 4 \geq 2x + 10
\]

Distribute the 3:

\[
3x + 3 + 4 \geq 2x + 10
\]

Combine like terms:

\[
3x + 7 \geq 2x + 10
\]

2. **Isolate the variable \( x \):**

Subtract \( 2x \) from both sides:

\[
3x - 2x + 7 \geq 10
\]

Simplify:

\[
x + 7 \geq 10
\]

Subtract 7 from both sides:

\[
x \geq 3
\]

3. **Express the solution in interval notation:**

The solution \( x \geq 3 \) means all values of \( x \) from 3 to infinity. In interval notation, this is:

\[
[3, \infty)
\]

So, the correct choice is:

**A. The solution is** \([3, \infty)\).

### Graph the Solution Set on a Number Line

To graph the solution set on a number line:

- Draw a number line.
- Place a closed dot at \( x = 3 \) (since the inequality is "greater than or equal to").
- Shade the line to the right of \( x = 3 \) to represent all numbers greater than or equal to 3.

Would you like to see the graph? Or do you have any other questions?

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### Related Questions

1. How do you solve inequalities with multiple variables?
2. What is the difference between an open and a closed interval?
3. How do you solve quadratic inequalities?
4. What are the rules for graphing inequalities on a number line?
5. How can you check the solution to an inequality?

**Tip:** Always verify your solutions by substituting back into the original inequality.

Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. 3(x + 1) + 4 >= 2x + 10. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is enter your response here. (Type the solution using interval notation.) B. The solution set is empty set.

Learn how to solve the linear inequality 3(x + 1) + 4 >= 2x + 10 step-by-step and express the solution in interval notation. This guide covers algebraic concepts such as solving inequalities and graphing them on a number line. Suitable for students in Grades 8-10.

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