what does the symbol mean in the problem 5x<3x+2

The symbol "<" in the inequality \( 5x < 3x + 2 \) means "less than." It indicates that the expression on the left side of the inequality, \( 5x \), is less than the expression on the right side, \( 3x + 2 \).

To solve this inequality, you can follow these steps:

1. Subtract \( 3x \) from both sides:
   \[
   5x - 3x < 2
   \]
   Simplifying this gives:
   \[
   2x < 2
   \]

2. Now, divide both sides by 2 to isolate \( x \):
   \[
   x < 1
   \]

So the solution to the inequality is \( x < 1 \), meaning \( x \) can take any value that is less than 1.

Do you have any questions or would you like more details?

Here are 5 related questions you might find useful:
1. What is the difference between "<" and ">" in inequalities?
2. How would you graph the solution \( x < 1 \)?
3. What happens if you multiply or divide both sides of an inequality by a negative number?
4. How do you solve inequalities involving fractions?
5. Can an inequality have more than one solution?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.

Explore how to understand and solve the inequality 5x < 3x + 2 with a detailed, step-by-step guide. Learn key algebraic concepts, including simplification techniques and properties of inequalities, suitable for students in Grades 6-8.

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