https://file.aiquickdraw.com/mathbot/file/17303241317653z8ql6qt.jpg

Let's go through each inequality one by one:

### 1. Solve \( 3x + 2 < 5 \)

1. Subtract 2 from both sides:
   \[
   3x < 3
   \]

2. Divide both sides by 3:
   \[
   x < 1
   \]

So, the solution for the first inequality is:
\[
x < 1
\]

### 2. Solve \( 4x + 7 \geq 35 \)

1. Subtract 7 from both sides:
   \[
   4x \geq 28
   \]

2. Divide both sides by 4:
   \[
   x \geq 7
   \]

So, the solution for the second inequality is:
\[
x \geq 7
\]

### 3. Solve \( 7 < 2x - 5 \)

1. Add 5 to both sides:
   \[
   12 < 2x
   \]

2. Divide both sides by 2:
   \[
   6 < x
   \]
   or equivalently,
   \[
   x > 6
   \]

So, the solution for the third inequality is:
\[
x > 6
\]

### Final Answers

1. \( x < 1 \)
2. \( x \geq 7 \)
3. \( x > 6 \)

Would you like a more detailed breakdown, or do you have any questions?

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Here are 5 related questions to explore:

1. How do you solve inequalities with variables on both sides?
2. What changes when you multiply or divide an inequality by a negative number?
3. How can you check if your solution to an inequality is correct?
4. What does it mean when inequalities have no solutions?
5. How are solutions to compound inequalities found?

**Tip:** Always flip the inequality sign when you multiply or divide by a negative number!

Solve the inequalities:
1. 3x + 2 < 5
2. 4x + 7 >= 35
3. 7 < 2x - 5

Learn how to solve linear inequalities with a step-by-step solution. This tutorial covers solving inequalities like 3x + 2 < 5, 4x + 7 >= 35, and 7 < 2x - 5. Suitable for students in Grades 7-9.

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