Worksheet: Absolute Value Inequalities

In this worksheet, we will practice solving systems of inequalities involving absolute values graphically.

Q1:

Determine which region in the graph contains all the solutions to the following system of inequalities:

  • AB
  • BC
  • CE
  • DG
  • EF

Q2:

Which of the following systems of inequalities is represented in the diagram?

  • A
  • B
  • C
  • D
  • E

Q3:

Which region represents the system of inequalities

  • AC
  • BA
  • CD
  • DB

Q4:

Find the system of inequalities that forms the shaded area shown in the graph.

  • A 𝑦 ( 𝑥 3 ) + 1 2 , 𝑦 < 2 | 𝑥 + 3 | + 1
  • B 𝑦 ( 𝑥 + 3 ) + 1 2 , 𝑦 < 2 | 𝑥 3 | + 1
  • C 𝑦 ( 𝑥 + 3 ) 1 2 , 𝑦 < 2 | 𝑥 + 3 | + 1
  • D 𝑦 ( 𝑥 3 ) + 1 2 , 𝑦 < 2 | 𝑥 3 | + 1
  • E 𝑦 ( 𝑥 3 ) + 1 2 , 𝑦 < 2 | 𝑥 + 3 | 1

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