Math Problem Statement

1/2x-3>2

Solution

Let's solve the inequality step by step:

Given inequality:

12x3>2\frac{1}{2}x - 3 > 2

Step 1: Add 3 to both sides to isolate the term with xx:

12x>2+3\frac{1}{2}x > 2 + 3

12x>5\frac{1}{2}x > 5

Step 2: Multiply both sides by 2 to get rid of the fraction:

x>5×2x > 5 \times 2

x>10x > 10

Final Answer:

x>10x > 10

So, the solution is x>10x > 10.

Would you like a detailed explanation or have any further questions on this?

Here are 5 related questions you could explore:

  1. How do I solve inequalities involving fractions or decimals?
  2. What happens if the inequality has a negative number instead of a positive one?
  3. How do I graph the solution of an inequality on a number line?
  4. How would I solve a compound inequality like x3>2x - 3 > 2 and x+5<10x + 5 < 10?
  5. What is the difference between solving an inequality and solving an equation?

Tip: Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Inequality solving (addition, multiplication)

Theorems

Basic rules for solving inequalities

Suitable Grade Level

Grades 7-9