equations and inequalities

这是一篇关于equations and inequalities的思维导图，主要内容有expressions and formulas、Properties of real numbers、Solving equations等。

equations and inequalities

• expressions and formulas
  • Algebraic expression
    • Expressions that contain at least one variable
      • E.g.3x a+b-c
  • Operation order
    • BIDMAS
  • Formulas
    • A mathematical sentence that express the relationship between certain quantities
• Properties of real numbers
  • Numbers in groups
    • Natural number
      • N
    • Whole number
      • W
    • Rational numbers
      • Q
    • Integers
      • Z
    • Irrational numbers
      • I
    • Real numbers
      • R
  • Properties
    • Commutative
      • A+B=B+A
      • A*B=B*A
    • Associative
      • （a+b)+c=a+(b+c)
      • (a*b)*c=a*(b*c)
    • Identity
      • a+0=a=0+a
      • a*1=a=1*a
    • Inverse
      • a+(-a)=0
      • a*(1/a)=1
    • Closure
      • a+b is a real number
      • a*b is a real number
    • Distribution
      • a(b+c)=ab+ac
• Solving equations
  • properties of equalities
    • Reflexive
      • A=A
    • Symmetric
      • If a=b than b=a
    • Transitive
      • If a=b b=c than arc
    • Substitution
      • (1+6)x=21 7x=21 1+6=7
    • Addition
    • Subtraction
    • Division
    • Multiplication
  • Write verbal into algebraic expressions
    • A+B
      • The sum of a and b
      • A plus b
      • Add b to a
    • A-B
      • The difference between a and b
      • A minus b
      • Subtract b from a
      • Reduce a by b
    • ab
      • The product of a and b
      • A times b
      • A multiplied by b
      • Multiply a by b
    • A/B
      • The quotient of a and b
      • A divided by b
      • Divide a by b
• Solving absolute value equalities
  • Absolute value of a number
    • Its distance from 0 on a number line
      • a大于🟰0 绝对值a=a
      • a小于0 绝对值a=-a
  • lx-cl=r
• Solving inequalities
  • 小于等于
    • less than or equal to
    • No more than
    • Is at most
  • 小于
    • Less than
    • Fewer than
  • 大于等于
    • Greater than or equal to
    • Is at least
• Solving compound and absolute value inequalities
  • vocabulary
    • Union并集
    • Intersection交集
  • lax+bl大于c
    • Ax+b大于c
    • ax+b小于-c
  • lax+bl小于c
    • -c小于ax+b小于c