https://file.aiquickdraw.com/mathbot/file/1726454221584em4dqvdj.jpg

Let's solve the inequality and then graph the solution.

### Inequality:
\[
2 + 2x < -12
\]

#### Step 1: Subtract 2 from both sides
\[
2x < -12 - 2
\]
\[
2x < -14
\]

#### Step 2: Divide by 2 to isolate \(x\)
\[
x < \frac{-14}{2}
\]
\[
x < -7
\]

### Inequality Notation:
\[
x < -7
\]

### Graphing:
On the number line, you'd plot an open circle at \(x = -7\) to indicate that \(-7\) is not included in the solution. Then shade everything to the left of \(-7\) because the inequality is \(x < -7\).

Would you like more details or further clarification?

Here are some related questions:
1. How would the solution change if the inequality were \(2 + 2x \leq -12\)?
2. Can you explain why dividing by a positive number doesn't flip the inequality?
3. How do you graph a solution for \(x \geq -7\)?
4. What is the solution to the inequality \(2 + 2x > -12\)?
5. How do you solve an inequality if you have a fraction, like \(\frac{2}{x} < 3\)?

**Tip**: Always remember that dividing or multiplying by a negative number flips the inequality sign!

Solve the inequality and graph the solution on the line provided: 2 + 2x < -12

Learn how to solve the linear inequality 2 + 2x < -12 step by step. This problem demonstrates the basic principles of solving inequalities by isolating the variable. Suitable for students in Grades 7-9, this solution includes inequality notation and a graph representation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation