Math Problem Statement
Solve each inequality analytically, writing the solution set in interval notation. (a) 6 - (x + 4) < 0, (b) 6 - (x + 4) ≥ 0
Solution
The problem involves solving two inequalities analytically and expressing the solution in interval notation:
Problem:
Solve each inequality analytically, writing the solution set in interval notation.
- (a)
- (b)
The hint suggests that part (b) can be solved based on part (a)'s answer.
Solution:
Part (a):
- Simplify the expression: So the inequality becomes:
- Solve for : Which means:
- The solution set for part (a) in interval notation is:
Part (b):
- From part (a), we already simplified to , so the inequality becomes:
- Solve for : Which means:
- The solution set for part (b) in interval notation is:
Final Answer:
- Part (a):
- Part (b):
Would you like further details on how to graph these solutions?
Here are 5 related questions for practice:
- How do you graph inequalities like on a number line?
- What is the difference between strict inequalities (<, >) and non-strict inequalities (≤, ≥)?
- How can we check if a specific value satisfies an inequality?
- Can inequalities have more than one solution? If so, how do you combine the solutions?
- What happens to the inequality sign when you multiply or divide by a negative number?
Tip: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Interval Notation
Formulas
Linear Inequalities
Theorems
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Suitable Grade Level
Grades 8-10