Math Problem Statement

x<2a+2b2x<\frac{2a+2b}{2}

Solution

The inequality you've written is:

x<2a+2b2x < \frac{2a + 2b}{2}

Let's simplify the right-hand side:

2a+2b2=a+b\frac{2a + 2b}{2} = a + b

So the inequality becomes:

x<a+bx < a + b

This means that xx is less than the sum of aa and bb.

Would you like further details or have any questions about this inequality?

Here are 5 related questions:

  1. How would we solve for xx if this inequality were part of a larger equation?
  2. What happens if the inequality was xa+bx \leq a + b instead of x<a+bx < a + b?
  3. How would this inequality be represented on a number line?
  4. Can we apply this inequality to a system of inequalities? How would we solve that system?
  5. What are some practical examples where this inequality might be used?

Tip: When working with inequalities, always remember to flip the sign when multiplying or dividing by a negative number.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Simplification

Formulas

\frac{2a + 2b}{2} = a + b

Theorems

Basic Properties of Inequalities

Suitable Grade Level

Grades 6-8