https://peda.net/id/e8576cf0bf2 2019-08-15T10:11:31+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/053e4da8c00 2019-08-16T11:44:12+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3x-1%5Cright%7C%5Cge%5Cleft%7Cx%2B2%5Cright%7C%5C%20%5C%20%5C%20%5C%20%5C%20%5Cmid%5E2" alt="\left|3x-1\right|\ge\left|x+2\right|\ \ \ \ \ \mid^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=9x%5E2-6x%2B1%5Cge%20x%5E2%2B4x%2B4" alt="9x^2-6x+1\ge x^2+4x+4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=8x%5E2-10x-3%5Cge0" alt="8x^2-10x-3\ge0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-%5Cleft(-10%5Cright)%5Cpm%5Csqrt%7B%5Cleft(-10%5Cright)%5E2-4%5Ccdot8%5Ccdot%5Cleft(-3%5Cright)%7D%7D%7B2%5Ccdot8%7D" alt="x=\frac{-\left(-10\right)\pm\sqrt{\left(-10\right)^2-4\cdot8\cdot\left(-3\right)}}{2\cdot8}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B10%5Cpm%5Csqrt%7B100%2B96%7D%7D%7B16%7D" alt="x=\frac{10\pm\sqrt{100+96}}{16}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B10%5Cpm14%7D%7B16%7D" alt="x=\frac{10\pm14}{16}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ctext%7Bx%7D%3D1%5C%20%5Cfrac%7B1%7D%7B2%7D%5C%20tai%5C%20x%3D-%5Cfrac%7B1%7D%7B4%7D" alt="\text{x}=1\ \frac{1}{2}\ tai\ x=-\frac{1}{4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=kuvaaja%5C%20on%5C%20yl%C3%B6sp%C3%A4in%5C%20aukeava%5C%20paraabeli%5C%20toisen%5C%20asteen%5C%20ter%5Cmin%5C%20ollessa%5C%20positiivinen" alt="kuvaaja\ on\ ylöspäin\ aukeava\ paraabeli\ toisen\ asteen\ ter\min\ ollessa\ positiivinen"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge1%5C%20%5Cfrac%7B1%7D%7B2%7D%5C%20tai%5C%20x%5Cle-%5Cfrac%7B1%7D%7B4%7D" alt="x\ge1\ \frac{1}{2}\ tai\ x\le-\frac{1}{4}"/><br/> <br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C1%2Bx%5Cright%7C%3E%5Cleft%7C3-4x%5Cright%7C%5C%20%5C%20%5C%20%5C%20%5C%20%5Cmid%5E2" alt="\left|1+x\right|&gt;\left|3-4x\right|\ \ \ \ \ \mid^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2x%2B1%3E16x%5E2-24x%2B9" alt="x^2+2x+1&gt;16x^2-24x+9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-15x%5E2%2B26x-8%3E0" alt="-15x^2+26x-8&gt;0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-26%5Cpm%5Csqrt%7B26%5E2-4%5Ccdot%5Cleft(-15%5Cright)%5Ccdot%5Cleft(-8%5Cright)%7D%7D%7B2%5Ccdot%5Cleft(-15%5Cright)%7D" alt="x=\frac{-26\pm\sqrt{26^2-4\cdot\left(-15\right)\cdot\left(-8\right)}}{2\cdot\left(-15\right)}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-26%5Cpm14%7D%7B-30%7D" alt="x=\frac{-26\pm14}{-30}"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-%5Cfrac%7B2%7D%7B5%7D%5C%20tai%5C%20x%3D-1%5Cfrac%7B1%7D%7B3%7D" alt="x=-\frac{2}{5}\ tai\ x=-1\frac{1}{3}"/></div> <div>toisen asteen termin kerroin on negatiivinen, kuvaaja on alaspäin aukeava paraabeli</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-1%5Cfrac%7B1%7D%7B3%7D%3Cx%3C-%5Cfrac%7B2%7D%7B5%7D" alt="-1\frac{1}{3}&lt;x&lt;-\frac{2}{5}"/></div> 2019-08-16T11:44:12+03:00 https://peda.net/id/312a6638c00 2019-08-16T11:31:06+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%2B1%5Cright%7C%3C%5Cleft%7Cx-2%5Cright%7C%5C%20%5C%20%5C%20%5Cmid%5E2" alt="\left|x+1\right|&lt;\left|x-2\right|\ \ \ \mid^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Cright%7Cx%2B1%5Cleft%7C%5Cright)%5E2-%5Cleft(%5Cright%7Cx-2%5Cleft%7C%5Cright)%5E2%3C0" alt="\left(\right|x+1\left|\right)^2-\left(\right|x-2\left|\right)^2&lt;0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2x%2B1%3Cx%5E2-4x%2B4" alt="x^2+2x+1&lt;x^2-4x+4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%3C3" alt="6x&lt;3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C%5Cfrac%7B1%7D%7B2%7D" alt="x&lt;\frac{1}{2}"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2-2x%5Cright%7C%5Cge%5Cleft%7C5%2B2x%5Cright%7C%5C%20%5C%20%5C%20%5Cmid%5E2" alt="\left|2-2x\right|\ge\left|5+2x\right|\ \ \ \mid^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%5E2-8x%2B4%5Cge4x%5E2%2B20x%2B25" alt="4x^2-8x+4\ge4x^2+20x+25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-28x-21%5Cge0" alt="-28x-21\ge0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-28x%5Cge21" alt="-28x\ge21"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle-%5Cfrac%7B3%7D%7B4%7D" alt="x\le-\frac{3}{4}"/> 2019-08-16T11:31:06+03:00 https://peda.net/id/60b512ecbff 2019-08-16T11:18:07+03:00 a) epätosi, 1/3 on suurempi kuin 1/4<br/> b) tosi, 0,99-1=-0,01 on pienempi kuin 0,01<br/> c) epätosi, |-0,02|=0,02 on suurempi kuin 0,01 ja siten toteuttaa epäyhtälön 2019-08-16T11:18:07+03:00 https://peda.net/id/9f295656bff 2019-08-16T11:12:42+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx-5%5Cright%7C%5Cle3" alt="\left|x-5\right|\le3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-5%5Cle3" alt="x-5\le3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle8" alt="x\le8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-5%5Cge-3" alt="x-5\ge-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge2" alt="x\ge2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cle%20x%5Cle8" alt="2\le x\le8"/><br/> <br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%2B2%5Cright%7C%3E7" alt="\left|x+2\right|&gt;7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B2%3E7" alt="x+2&gt;7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E5" alt="x&gt;5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B2%3C-7" alt="x+2&lt;-7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C-9" alt="x&lt;-9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=tai" alt="tai"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E5" alt="x&gt;5"/> 2019-08-16T11:12:42+03:00 https://peda.net/id/e518ad34bff 2019-08-16T11:08:55+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx-2%5Cright%7C%5Cge5" alt="\left|x-2\right|\ge5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-2%5Cge5" alt="x-2\ge5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge7" alt="x\ge7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-2%5Cle-5" alt="x-2\le-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle-3" alt="x\le-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=tai" alt="tai"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge7" alt="x\ge7"/> 2019-08-16T11:07:30+03:00 https://peda.net/id/a1e43896bff 2019-08-16T11:04:36+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-x%2B1%5Cright%7C%3E2" alt="\left|-x+1\right|&gt;2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%2B1%3E2" alt="-x+1&gt;2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3E1" alt="-x&gt;1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C-1" alt="x&lt;-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%2B1%3C-2" alt="-x+1&lt;-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3C-3" alt="-x&lt;-3"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3E3" alt="x&gt;3"/></div> <div>tai</div> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C-1" alt="x&lt;-1"/><br/> <br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C7-x%5Cright%7C%3C-1" alt="\left|7-x\right|&lt;-1"/><br/> epäyhtälöllä ei ole ratkaisuja, itseisarvo ei voi olla negatiivinen<br/> <div><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C6x-3%5Cright%7C%5Cge7" alt="\left|6x-3\right|\ge7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x-3%5Cge7" alt="6x-3\ge7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%5Cge10" alt="6x\ge10"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge1%5C%20%5Cfrac%7B2%7D%7B3%7D" alt="x\ge1\ \frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x-3%5Cle-7" alt="6x-3\le-7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%5Cle-4" alt="6x\le-4"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle-%5Cfrac%7B2%7D%7B3%7D" alt="x\le-\frac{2}{3}"/></div> <div>tai</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge1%5C%20%5Cfrac%7B2%7D%7B3%7D" alt="x\ge1\ \frac{2}{3}"/><br/> <br/> <br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C4x%2B2%5Cright%7C%5Cge0" alt="\left|4x+2\right|\ge0"/></div> <div>epäyhtälö on tosi kaikilla x arvoilla, jotka ovat reaalilukuja</div> </div> </div> 2019-08-16T10:51:19+03:00 https://peda.net/id/92593026bff 2019-08-16T10:43:43+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C6x%2B1%5Cright%7C%3C3" alt="\left|6x+1\right|&lt;3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3%3C6x%2B1%3C3" alt="-3&lt;6x+1&lt;3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-4%3C6x%3C2" alt="-4&lt;6x&lt;2"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-%5Cfrac%7B2%7D%7B3%7D%3Cx%3C%5Cfrac%7B1%7D%7B3%7D" alt="-\frac{2}{3}&lt;x&lt;\frac{1}{3}"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C5-12x%5Cright%7C%3E9" alt="\left|5-12x\right|&gt;9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5-12x%3E9" alt="5-12x&gt;9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-12x%3E4" alt="-12x&gt;4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C-%5Cfrac%7B1%7D%7B3%7D" alt="x&lt;-\frac{1}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5-12x%3C-9" alt="5-12x&lt;-9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-12x%3C-14" alt="-12x&lt;-14"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E1%5C%20%5Cfrac%7B1%7D%7B6%7D" alt="x&gt;1\ \frac{1}{6}"/><br/> tai <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C-%5Cfrac%7B1%7D%7B3%7D" alt="x&lt;-\frac{1}{3}"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C4x%5Cright%7C%5Cle2" alt="\left|4x\right|\le2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%5Cle2" alt="4x\le2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle%5Cfrac%7B1%7D%7B2%7D" alt="x\le\frac{1}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%5Cge-2" alt="4x\ge-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge-%5Cfrac%7B1%7D%7B2%7D" alt="x\ge-\frac{1}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-%5Cfrac%7B1%7D%7B2%7D%5Cle%20x%5Cle%5Cfrac%7B1%7D%7B2%7D" alt="-\frac{1}{2}\le x\le\frac{1}{2}"/><br/>  <br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-3x%2B7%5Cright%7C%5Cge2" alt="\left|-3x+7\right|\ge2"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=-3x%2B7%5Cge2" alt="-3x+7\ge2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%5Cge-5" alt="-3x\ge-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle1%5C%20%5Cfrac%7B2%7D%7B3%7D" alt="x\le1\ \frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%2B7%5Cle-2" alt="-3x+7\le-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%5Cle-9" alt="-3x\le-9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge3" alt="x\ge3"/></div> <div>tai</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle1%5C%20%5Cfrac%7B2%7D%7B3%7D" alt="x\le1\ \frac{2}{3}"/></div> <div> </div> </div> 2019-08-16T10:43:43+03:00 https://peda.net/id/02986404bff 2019-08-16T10:25:23+03:00 a) itseisarvo ei voi olla negatiivinen<br/> b) itseisarvo on aina nolla tai positiivinen<br/> c) itseisarvon, minkä tahansa luvun neliön ja positiivinen kokonaisluvun summa on positiivinen<br/> d) koska vain |0| voi olla nolla tai pienempi 2019-08-16T10:25:23+03:00 https://peda.net/id/552ff8a4bff 2019-08-16T10:20:32+03:00 <p>A3<br/> B2<br/> C4<br/> D1</p> 2019-08-16T10:20:32+03:00 https://peda.net/id/81bb1e7cbff 2019-08-16T10:14:37+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5Cright%7C%3C2" alt="\left|x\right|&lt;2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C2" alt="x&lt;2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E-2" alt="x&gt;-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-2%3Cx%3C2" alt="-2&lt;x&lt;2"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C6x%5Cright%7C%3C24" alt="\left|6x\right|&lt;24"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%3C24" alt="6x&lt;24"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C4" alt="x&lt;4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%3E-24" alt="6x&gt;-24"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E-4" alt="x&gt;-4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-4%3Cx%3C4" alt="-4&lt;x&lt;4"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C5x%2B10%5Cright%7C%5Cle20" alt="\left|5x+10\right|\le20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5x%2B10%5Cle20" alt="5x+10\le20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5x%5Cle10" alt="5x\le10"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cle2" alt="x\le2"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=5x%2B10%5Cge-20" alt="5x+10\ge-20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5x%5Cge-30" alt="5x\ge-30"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cge-6" alt="x\ge-6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-6%5Cle%20x%5Cle20" alt="-6\le x\le20"/><br/> <br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-2x%5Cright%7C%3C5" alt="\left|3-2x\right|&lt;5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3-2x%3C5" alt="3-2x&lt;5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-2x%3C2" alt="-2x&lt;2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3E-1" alt="x&gt;-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3-2x%3E-5" alt="3-2x&gt;-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-2x%3E-8" alt="-2x&gt;-8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3C4" alt="x&lt;4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-1%3Cx%3C4" alt="-1&lt;x&lt;4"/></div> 2019-08-16T10:14:37+03:00