Math Problem Statement

حلش کن

Solve the inequalities: x - 1 > 4 and x + 1 < 2

Solution

From the image, I can see two inequalities written in Arabic numerals, which I'll interpret as follows:

  1. The first inequality appears to be:

x1>4x - 1 > 4

  1. The second inequality seems to be:

x+1<2x + 1 < 2

Now, let's solve these inequalities one by one.

Inequality 1: x1>4x - 1 > 4

Add 1 to both sides:

x>4+1x > 4 + 1

x>5x > 5

Inequality 2: x+1<2x + 1 < 2

Subtract 1 from both sides:

x<21x < 2 - 1

x<1x < 1

Solution

The solution to these two inequalities is that xx must satisfy both conditions: x>5x > 5 and x<1x < 1.

However, there's no number xx that is both greater than 5 and less than 1, so no solution exists where these two inequalities are true simultaneously.

Let me know if you would like more details or if you have further questions.

Here are 5 relative questions:

  1. How do we represent inequalities on a number line?
  2. Can inequalities have a solution with no overlap, as in this case?
  3. What are the rules for solving compound inequalities?
  4. How would the solution change if the inequalities were non-strict (i.e., \geq and \leq)?
  5. Can you think of a scenario where such inequalities would have a real-life application?

Tip: Always check for contradictions when solving inequalities to avoid incorrect conclusions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Compound Inequalities

Formulas

Solving linear inequalities

Theorems

Properties of inequalities

Suitable Grade Level

Grades 7-9