Math Problem Statement

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation. [x+7<x+2]

Solution

Let's solve the compound inequality step by step.

Given inequality:

x+7<x+2x + 7 < x + 2

Step 1: Subtract xx from both sides

(x+7)x<(x+2)x(x + 7) - x < (x + 2) - x This simplifies to: 7<27 < 2

Step 2: Analyze the result

The inequality 7<27 < 2 is false. Since there is no value of xx that makes this inequality true, the solution is no solution.

Answer:

There is no solution to the inequality. In interval notation, the solution is represented as the empty set, which can be written as: or()\emptyset \quad \text{or} \quad ( )

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

  1. How do you solve an inequality involving both "<" and "≤" signs?
  2. What are the steps for solving compound inequalities with multiple parts?
  3. How do you express a solution when the inequality holds for all values of xx?
  4. How do you handle compound inequalities involving "and" versus "or"?
  5. What is the graphical interpretation of a solution with no valid xx?

Tip: Always check if a simplified inequality results in a contradiction (like 7<27 < 2) or a true statement (like 7>27 > 2) to determine if there are solutions or not.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Algebra

Formulas

Basic inequality solving steps

Theorems

Properties of inequalities

Suitable Grade Level

Grades 6-8