Copy of 1.4 Solving Absolute Inequalities (Due 10/23/25) (10/21/2025)

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.

Day 1 10/21/24

Required

20

Solve, graph, and write the solutions to the following inequalities in interval notation.

_______ U_______

Required

20

Solve, graph, and write the solutions to the following inequalities in interval notation.

20

Solve, graph, and write the solutions to the following inequalities in interval notation.

_______U_______ 

Required

20

Solve, graph, and write the solutions to the following inequalities in interval notation.

Required

20

Solve, graph, and write the solutions to the following inequalities in interval notation.

Spiral Review

Required

10

Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.

A.CED.1

A.SSE.1.b

Required

10

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?)
 _______

A.CED.1

A.SSE.1.b

Required

2

Is this an open or closed interval?

Required

2

Is this an open or closed interval?

Required

2

Is this an open or closed interval?

Required

2

Is this an open or closed interval?

Required

5

Use interval notation to describe the range of this function.

Required

5

Use interval notation to describe the domain of this function.

Required

5

Write the following in interval notation.

Required

5

Write the following in interval notatin.

Required

12

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

(-∞,-2)∪(2,∞)
|x|<2

Required

12

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

-3≤x≤13
|x-5|<8

Required

12

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

1<x≤4
(1,4]

Required

8

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

5<x≤9
x<5 or x≥9
(-∞,5)∪[9,∞)
(5,9)

Day 2 10/22/25

More Solving Absolute Value Inequalities

Required

20

Solve and graph the inequality

Required

20

Solve and graph the inequality:

Required

20

Solve and graph the inequality:

Required

20

Solve and graph.

Required

20

Solve and graph the inequality:

Day 3 10/23/25

Graphing Absolute Value Functions

Required

10

Use a set of x values to graph the parent function y=|x|

Required

10

Use a set of x values to graph the function y=|x|+ 2

Required

10

Compare the graph y=|x|to y=|x|+ 2

How are they the same?
_______ 

How are they different?
_______ 

Required

10

Use a set of x values to graph the function y=|x - 2|

Required

10

Compare the graph y=|x| to  y=|x  -  2|

How are they the same?
_______ 

How are they different?
_______ 

Required

10

Make a prediction. What will the graph of y=|x - 2|+ 2 look like?

Required

10

Use a set of x values to graph the function y=|x - 2|+ 2

Day 5 10/15/24

Graphing Absolute Value part 2

Required

10

Notes: Critical Values of Absolute Value Functions

Required

20

1)What are the critical values of this absolute value function:

y=|x-1|+2

Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

Required

8

What are the critical values of this absolute value function:

y=2|x+2|+2

Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

Required

8

What are the critical values of this absolute value function:




Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

Required

8

What are the critical values of this absolute value function:




Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

Required

8

What are the critical values of this absolute value function:




Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

Day 6 10/16/24

More Graphing Absolute Value 

Required

8

How is the absolute function below different than the parent function y=|x|:

y=|x-1|+2

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Required

8

How is the absolute function below different than the parent function y=|x|:

y=2|x+6|-2

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Required

8

How is the absolute function below different than the parent function y=|x|:

y=-3|x-4|-9

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Required

8

How is the absolute function below different than the parent function y=|x|:

y=1/2|x+3|+1

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Required

8

How is the absolute function below different than the parent function y=|x|:

y=-1/3|x-5|-5

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Required

8

How is the absolute function below different than the parent function y=|x|:

y=.5|x-8|+3

Opens (Upward or Downward) _______ 

Horizontal Shift (write none if there is none) _______ 

Vertical Shift (write none if there is none) _______ 

Stretched (0<|a|<1), Compressed (|a|>1), or None  _______.

Spiral Review

Required

5

Simplify each radical

Required

5

Simplify each radical

Required

5

Simplify this expression. Your answer should not have negative exponents.

Required

5

Simplify this expression. Your answer should not have negative exponents.

Required

5

Simplify this expression. Your answer should not have negative exponents.

Required

10

Find the Product of these polynomials.

Required

10

Find the Product of these polynomials.

Required

10

Find the Product

Required

10

Find the Product:

Day 7 10/18/24

Real World Applications

Required

20

Sam is sitting in a boat on a lake. She can get burned by the sunlight that hits her directly and by sunlight that reflects off the water. Sunlight reflects off the water at the point (2, 0) and hits Sam at the point (3.5, 3). Write and graph the function that shows the path of the sunlight.

1) Graph the function

2) Write the function that shows the path of the sunlight.

_______

Required

20

A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in inches per hour) at which it rains is given by the function r = −0.5 ⎜t − 1⎟ + 0.5, where t is the time (in hours). Graph the function. Determine for how long it rains and when it rains the hardest.

Opens (upward or downward)
_______ 
Axis of Symmetry
_______ 
Vertex
_______ 
Slope
_______ 

2) Use the critical values of this equation to graph it.

3) Determine for how long it rains 
_______ 

and when it rains the hardest.
_______

Required

20

While playing pool, a player tries to shoot the eight ball into the corner pocket as shown. Imagine that a coordinate plane is placed over the pool table. The eight ball is at (5, 5/4) and the pocket they are aiming for is at (10, 5). The player is going to bank the ball off the side at (6, 0).

2) Write an equation for the path of the ball.
 
3) Did the player make the shot? How do you know?
_______

Required

10

Copy of 1.4 Solving Absolute Inequalities (Due 10/23/25) (10/21/2025)

Day 1 10/21/24

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.

Spiral Review

Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.

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)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Day 2 10/22/25

More Solving Absolute Value Inequalities

Solve and graph the inequality

Solve and graph the inequality:

Solve and graph the inequality:

Solve and graph.

Solve and graph the inequality:

Day 3 10/23/25

Graphing Absolute Value Functions

Use a set of x values to graph the parent function y=|x|

Use a set of x values to graph the function y=|x|+ 2

Use a set of x values to graph the function y=|x - 2|

Make a prediction. What will the graph of y=|x - 2|+ 2 look like?

Use a set of x values to graph the function y=|x - 2|+ 2

Day 5 10/15/24

Graphing Absolute Value part 2

Notes: Critical Values of Absolute Value Functions

Day 6 10/16/24

More Graphing Absolute Value

Spiral Review

Simplify each radical

Simplify each radical

Simplify this expression. Your answer should not have negative exponents.

Simplify this expression. Your answer should not have negative exponents.

Simplify this expression. Your answer should not have negative exponents.

Find the Product of these polynomials.

Find the Product of these polynomials.

Find the Product of these polynomials.

Find the Product of these polynomials.

Find the Product

Find the Product

Find the Product:

Find the Product:

Day 7 10/18/24

Real World Applications

Explain the Error Explain why the graph shown is not the graph of y = ⎜x + 3⎟ + 2. What is the correct equation shown in the graph?

Day 1 10/21/24

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.

Spiral Review

Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.

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)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

Day 2 10/22/25

More Solving Absolute Value Inequalities

Solve and graph the inequality

Solve and graph the inequality:

Solve and graph the inequality:

Solve and graph.