Is this an open or closed interval?
Is this an open or closed interval?
Essential Question:How can we solve and interpret absolute value inequalities to find the range of possible solutions?
Learning Target: Students will be able to solve absolute value inequalities and represent their solutions on a number line, understanding how the inequality affects the direction and type of solution set (e.g., union of intervals or a bounded interval).
Show your work for credit.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Solve, graph, and write the solutions to the following inequalities in interval notation.
Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.
Compare and Contrast: Explain the similarities and differences in solving these inequalities |x - 1| ≤ 2 and |x - 1| ≥ 2.
Compare these two inequalities. (How are they alike?)
Contrast these two inequalities. (How are they different?)
Is this an open or closed interval?
Is this an open or closed interval?
Is this an open or closed interval?
Is this an open or closed interval?
Use interval notation to describe the range of this function.
Use interval notation to describe the domain of this function.
Write the following in interval notation.
Write the following in interval notatin.
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
x<-2 or x>2
|x|>2
-2<x<2
(-2,2)
|x|≤2
|x|<2
|x|≥2
(-∞,-2)∪(2,∞)
-2≤x≤2
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
-3≤x≤13
x<-4 or x>4
[-3,13]
(-∞,-4)∪(4,∞)
(-3,13)
|x|<4
x≤-4 or x≥4
|x-5|<8
|x|>4
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
(-∞,3)∪(5,∞)
|x-2.5|<1.5
1>x≤4
|x-4|>1
1<x≤4
x<3 or x>5
x<1 or x≥4
(1,4]
3<x<5
Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)
5<x≤9
(-∞,5)∪[9,∞)
x≤5 or x>9
(5,9)
(5,9]
(-∞,5]∪(9,∞)
x<5 or x≥9
Solve and graph the inequality
Solve and graph the inequality:
Solve and graph the inequality:
Solve and graph.
Solve and graph the inequality:
