2.3.7

Set Notation & Inequalities

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How is Set Notation used with Inequalities?

Set notation can be used to represent the solutions of an inequality.

Illustrative background for What is the set notation for an inequality?Illustrative background for What is the set notation for an inequality? ?? "content

What is the set notation for an inequality?

  • Let's consider the inequality x>1x>1.
  • The solutions to this inequality are all of the values of xx that are greater than 1.
  • More formally, the solution is the set of all values of xx such that x>1x>1.
    • We can write this as {x:x>1x:x>1}
Illustrative background for What is the set notation for two inequalities?Illustrative background for What is the set notation for two inequalities? ?? "content

What is the set notation for two inequalities?

  • Let's consider the inequalities x<0x<0 and x>2x>2.
  • The solutions to these inequalities are all of the values of xx that are less than 0 and greater than 2.
  • We can also think of the solution as the union of the set of all values of xx such that x<0x<0 and the set of all values of xx such that x>2x>2.
Illustrative background for $$x<0$$ and 
$$x>2$$Illustrative background for $$x<0$$ and 
$$x>2$$ ?? "content

x<0x<0 and x>2x>2

  • We can write this in set notation as:
    • {x:x<0x:x\lt0} {x:x>2x:x\gt2}
Illustrative background for What is the set notation for two inequalities?Illustrative background for What is the set notation for two inequalities? ?? "content

What is the set notation for two inequalities?

  • Let's consider the inequality 1x31 \leq x \leq 3.
  • The solutions to this inequality are all of the values of xx that are greater than or equal to 1 and less than or equal to 3.
    • In set notation we can write this as {x:1x3x:1 \leq x \leq 3}.
Illustrative background for $$1 \leq x \leq 3$$Illustrative background for $$1 \leq x \leq 3$$ ?? "content

1x31 \leq x \leq 3

  • We can also think of the solution as the intersection of the set of all values of xx such that x1x\geq1 and the set of all values of xx such that x3x\leq3.
  • We can write this in set notation as:
    • {x:x1x:x\geq1} {x:x3x:x\leq3}

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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