algebra solving absolute value equations and inequalities
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  • 1. Ix+3I=4
    Ix+3I≥4
    Solve absolute equalities
    and inequalities
    Ix+3I<4
  • 2. IxI=4
    x=4 ,x=-4
    Those are your 2 answers
    X=4,-4
    Now GRAPH….
  • 3. Graph IxI=4
    Points (-4,4)
    -4
    4
    0
  • 4. Ix+3I=4
    x+3=4 ,x+3=-4
    X+3=-4
    -3 -3
    -7
    x=-7
    X+3=4
    -3 -3
    1
    x=1
    X=-7,1
    • Now CHECK….
  • Ix+3I=4
    x+3=4 ,x+3=-4
    Plug in 1 for x.
    1+3=4
    4=4
    Plug in -7 for x.
    -7+3=-4
    -4=-4
    X=-7,1
    • Now GRAPH….
  • Graph Ix+3I=4
    Points (-7,1)
    -7 1
    0
  • 5. Ix+5I>4
    x+5>4 , x+5<-4
    -5 -5
    -1
    X>-1
    -5 -5
    -9
    X<-9
    x<-9,X>-1 or (-∞,-9)U(-1,∞)
    • Now CHECK….
  • Ix+5I>4
    x+5>4 , x+5<-4
    Plug in anything
    less than -9 for x.
    Like -10.
    -10+5<-4
    -5<-4
    Plug in anything
    greater than -1 for x.
    Like 0.
    0+5>4
    5>4
    x<-9,X>-1 or (-∞,-9)U(-1,∞)
    • Now GRAPH….
  • Graph Ix+5I>4
    Open circles
    Because its
    Less than and
    Greater than.
    Not equal too.
    Points (-9,-1)
    x<-9 x>-1
    0
  • 6. Ix+5I≥4
    x+5≥4 , x+5≤-4
    -5 -5
    -1
    X≥-1
    -5 -5
    -9
    X≤-9
    x≤-9,X≥-1 or (-∞,-9]U[-1,∞)
    • Now CHECK….
  • Ix+5I≥4
    x+5≥4 , x+5≤-4
    Plug in anything
    less than -9 for x.
    Like -10.
    -10+5<-4
    -5<-4
    Plug in anything
    greater than -1 for x.
    Like 0.
    0+5>4
    5>4
    x<-9,X>-1 or (-∞,-9]U[-1,∞)
    • Now GRAPH….
  • Graph Ix+5I≥4
    Closed circles
    Because its
    Less than, equal
    too andGreater
    Than, equal too.
    Points (-9,-1)
    x≤-9 x≥-1
    0
  • 7. I2xI≥4
    2x≥4 , 2x≤-4
    2 2
    X≥2
    2 2
    X≤-2
    x≤-2,X≥2 or (-∞,-2]U[-2, ∞)
    • Now CHECK….
  • I2xI≥4
    2x≥4 , 2x≤-4
    Plug in anything
    less than -2 for x.
    Like -3.
    2(-3)≤-6
    -6≤-4
    Plug in anything
    greater than 2 for x.
    Like 3.
    2(3)≥4
    6≥4
    x≤-2,X≥2 or (-∞,-2]U[2, ∞)
    • Now GRAPH….
  • Graph I2xI≥4
    Closed circles
    Because its
    Less than, equal
    too andGreater
    Than, equal too.
    Points (-2,2)
    x≤-2 x≥2
    0
  • 8. I-2xI≥4
    -2x≥4 , -2x≤-4
    -2 -2
    X≥2
    -2 -2
    Now when you divide by a negative
    Number, you HAVE to flip the sign.
    X≤-2
    x≤-2,x≥2 or (-∞,-2]U[-2, ∞)
    • Now CHECK….
  • I-2xI≥4
    -2x≥4 , -2x≤-4
    Plug in anything
    greater than 2 for x.
    Like 3.
    -2(3)≤-4
    -6≤-4
    Plug in anything
    less than -2 for x.
    Like -3.
    -2(-3)≥6
    6≥4
    x≤-2,X≥2 or (-∞,-2]U[2, ∞)
    • Now GRAPH….
  • Graph I-2xI≥4
    Closed circles
    Because its
    Less than, equal
    too andGreater
    Than, equal too.
    Points (-2,2)
    x≤-2 x≥2
    0