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# 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 />