Math Problem Statement
Solve the inequality. Graph the solutions. StartAbsoluteValue x EndAbsoluteValueplus2greater than10
Solution
The inequality is:
Step 1: Isolate the absolute value term.
We start by subtracting 2 from both sides of the inequality:
Step 2: Break the absolute value inequality into two cases.
Since , the solutions will be when:
Step 3: Graph the solution.
The solution consists of all values of greater than 8 and less than -8. These are two open intervals:
On a number line, this would be represented by two rays extending to the left from and to the right from , with open circles at and , indicating that these points are not included in the solution.
Graph Description:
- A number line with two open circles at and .
- Arrows extending left from and right from , representing all values less than and greater than .
Would you like me to generate this graph for you?
Relative Questions:
- How do absolute value inequalities differ from regular inequalities?
- What happens when we reverse the inequality symbol (e.g., )?
- How would the solution change if the inequality was ?
- Can you solve a similar inequality, such as ?
- How do we graph compound inequalities on a number line?
Tip: Always isolate the absolute value term first when solving inequalities!
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Inequalities
Inequalities
Formulas
|x| > a when x > a or x < -a
Theorems
Absolute Value Theorem
Suitable Grade Level
Grades 8-10