What is the solution to the compound inequality in interval notation?

2(x+3)>6  or  2x+3≤−7

Let's solve the compound inequality step by step:

### 1st inequality: 
\[
2(x+3) > 6
\]
#### Step 1: Simplify the inequality.
\[
2(x+3) > 6 \quad \text{becomes} \quad 2x + 6 > 6
\]
#### Step 2: Subtract 6 from both sides.
\[
2x > 0
\]
#### Step 3: Divide by 2.
\[
x > 0
\]

### 2nd inequality: 
\[
2x + 3 \leq -7
\]
#### Step 1: Subtract 3 from both sides.
\[
2x \leq -10
\]
#### Step 2: Divide by 2.
\[
x \leq -5
\]

### Final solution:
The compound inequality is connected by **"or"**, meaning the solution is the union of both inequalities.

- The solution to \(x > 0\) is \((0, \infty)\).
- The solution to \(x \leq -5\) is \((-\infty, -5]\).

#### Interval Notation:
The solution to the compound inequality is the union of both intervals:
\[
(-\infty, -5] \cup (0, \infty)
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve compound inequalities connected by "and"?
2. What is the difference between "and" and "or" in compound inequalities?
3. How do you graph compound inequalities on a number line?
4. What are the steps to solve absolute value inequalities?
5. How can you check if a given value satisfies a compound inequality?

**Tip:** Always remember to handle each part of a compound inequality separately before combining them.

What is the solution to the compound inequality in interval notation? 2(x+3)>6 or 2x+3≤−7

Discover how to solve the compound inequality 2(x+3)>6 or 2x+3≤−7 in interval notation. This solution breaks down the steps for solving each inequality and explains how to combine them. Perfect for students in Grades 8-10 learning about algebra and compound inequalities.

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