To solve the inequality $2x + 3 > 11$, follow these steps:

Step 1: Isolate the variable $x$.

1. Subtract 3 from both sides of the inequality: $2x + 3 - 3 > 11 - 3$ $2x > 8$

2. Divide both sides by 2: $\frac{2x}{2} > \frac{8}{2}$ $x > 4$

Solution

The solution to the inequality is $x > 4$.

Step 2: Show the solution on a number line.

• Draw a number line.
• Mark the point 4 on the number line.
• Since the inequality is strictly greater than ($>$), we use an open circle at 4 to indicate that 4 is not included in the solution.
• Shade the number line to the right of 4 to represent all numbers greater than 4.

Here is how the number line should look:

$\text{---}( \, \text{4} \, \text{)}\text{========>}$

Do you want any more details or have any questions?

Here are some related questions:

1. How would you solve the inequality $3x - 5 < 10$?
2. Can you solve the compound inequality $2x + 3 > 11$ and $x - 1 \leq 7$?
3. What would change if the inequality was $2x + 3 \geq 11$?
4. How do you represent inequalities with less than ($<$) on a number line?
5. Can you graph $x > 4$ on a coordinate plane?

Tip: Always check the direction of the inequality when dividing or multiplying both sides by a negative number, as the inequality sign reverses in such cases.