Curriculum
Course: General Mathematics — Second Secondary
Login

Curriculum

General Mathematics — Second Secondary

Unit 1: Real Functions and Curve Sketching

0/10

Unit 2: Exponents, Logarithms and Applications

0/10

Unit 3: Limits

0/6

Unit 4: Trigonometry

0/4
Text lesson

Solving Equations and Inequalities

General Mathematics — Second Secondary

Solving Equations and Inequalities

Absolute value inequalities

Absolute value inequalities

  • For a positive number a:
Comparison aspectMain ideaKeywords
|x| < a
  • is equivalent to −a < x < a
  • so x lies inside an interval around zero
equivalentliesinsideinterval
|x| ≤ ais equivalent to −a ≤ x ≤ aequivalent
|x| > a
  • is equivalent to x > a or x < −a
  • so x lies outside the interval
equivalentliesoutsideinterval
|x| ≥ ais equivalent to x ≥ a or x ≤ −aequivalent
•
  • Note that the word “or” gives a union of two intervals
  • while “and” gives their intersection
Notewordgivesunion
•Write the solution with the correct notation for each caseWritesolutioncorrectnotation
Solving Equations and Inequalities · 2 / 6