2x+3>11 solve the inequality. Show the solution on a number line.

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.

Learn how to solve the inequality 2x + 3 > 11 step-by-step with a detailed explanation and number line representation. This problem covers key algebraic concepts such as inequalities and number line representation, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation