Solve the inequality. Write the solution set in interval notation.

2 left parenthesis x plus 4 right parenthesis plus 3 greater than or equals 7 plus 2 x

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Part 1

The solution set is

enter your response here

.

​(Type your answer in interval​ notation.)

Let's solve the inequality step by step:

### Given inequality:
\[
2(x + 4) + 3 \geq 7 + 2x
\]

### Step 1: Distribute the 2 on the left side.
\[
2x + 8 + 3 \geq 7 + 2x
\]
\[
2x + 11 \geq 7 + 2x
\]

### Step 2: Subtract \(2x\) from both sides.
\[
2x + 11 - 2x \geq 7 + 2x - 2x
\]
\[
11 \geq 7
\]

### Step 3: Simplify.
\[
11 \geq 7
\]

This is always true, meaning the inequality holds for all real numbers.

### Conclusion:
The solution set is all real numbers, so in interval notation, we write:
\[
(-\infty, \infty)
\]

Would you like more details on any part of this explanation?

### Related Questions:
1. How do we handle inequalities with fractions?
2. What are the rules for multiplying or dividing both sides of an inequality by a negative number?
3. How do we solve compound inequalities?
4. Can you explain how to graph solution sets of inequalities on a number line?
5. How do absolute value inequalities differ from regular inequalities?

**Tip:** When solving inequalities, if you multiply or divide both sides by a negative number, remember to reverse the inequality sign.

Solve the inequality. Write the solution set in interval notation.
2(x + 4) + 3 ≥ 7 + 2x

Learn how to solve the linear inequality 2(x + 4) + 3 ≥ 7 + 2x step by step, using the distributive property and properties of inequalities. This problem covers key algebraic concepts and is suitable for students in Grades 7-10.

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