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:
Step 1: Subtract from both sides
This simplifies to:
Step 2: Analyze the result
The inequality is false. Since there is no value of 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:
Would you like more details or have any questions?
Here are 5 related questions to further your understanding:
- How do you solve an inequality involving both "<" and "≤" signs?
- What are the steps for solving compound inequalities with multiple parts?
- How do you express a solution when the inequality holds for all values of ?
- How do you handle compound inequalities involving "and" versus "or"?
- What is the graphical interpretation of a solution with no valid ?
Tip: Always check if a simplified inequality results in a contradiction (like ) or a true statement (like ) 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