Math Problem Statement
Solution
To solve the inequalities using the given graphs of and , let's analyze the intersection and relative positions of the two lines:
- The blue line represents and the red line represents .
- The lines intersect at the point .
Now, we will solve the three parts based on this information:
(a)
This happens at the point where the two lines intersect, which is at .
Solution: in set notation or in interval notation.
(b)
The blue line () is greater than the red line () to the left of the intersection, i.e., when .
Solution:
(c)
This inequality holds where is less than or equal to , which occurs when .
Solution:
Would you like more details on any of the steps? Here are 5 related questions:
- How do we find the intersection of two lines algebraically?
- What methods can be used to solve linear inequalities graphically?
- How would the solution change if the slope of one of the lines was different?
- What is the significance of the interval notation used in inequalities?
- Can you always determine inequalities between lines by looking at their graphs?
Tip: When solving inequalities graphically, always pay attention to the intersection points, as they often mark transitions in the inequality signs.
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Graphing
Coordinate Geometry
Formulas
-
Theorems
Intersection Theorem
Graphical Solution of Inequalities
Suitable Grade Level
Grades 9-12
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