Ix+3I=4<br />Ix+3I≥4<br />Solve absolute equalities<br /> and inequalities<br />Ix+3I<4<br />
IxI=4<br />x=4			,x=-4<br />Those are your 2 answers<br />X=4,-4<br />Now GRAPH….<br />
Graph IxI=4<br />Points (-4,4)<br />-4<br />4<br />0<br />
Ix+3I=4<br />x+3=4			,x+3=-4<br />    X+3=-4<br />        -3  -3<br />             -7<br />    x=-7<br />     X+3=4<br /> ...
Ix+5I>4<br />x+5>4			, x+5<-4<br />-5  -5<br />    -1<br />X>-1<br />-5  -5<br />    -9<br />X<-9<br />x<-9,X>-1   or  (-∞...
Ix+5I≥4<br />x+5≥4			, x+5≤-4<br />-5  -5<br />    -1<br />X≥-1<br />-5  -5<br />    -9<br />X≤-9<br />x≤-9,X≥-1   or  (-∞...
I2xI≥4<br />2x≥4			, 2x≤-4<br />2    2<br />X≥2<br />2    2<br />X≤-2<br />x≤-2,X≥2   or  (-∞,-2]U[-2, ∞)<br /><ul><li>Now...
I-2xI≥4<br />-2x≥4			, -2x≤-4<br />-2    -2<br />X≥2<br />-2    -2<br />Now when you divide by a negative<br />Number, you...
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
algebra solving absolute value equations and inequalities
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algebra solving absolute value equations and inequalities

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

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