https://peda.net/id/c044d6b8bda 2019-08-13T12:43:05+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/61bbe3e6bf3 2019-08-15T10:51:26+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%2B1%5Cright%7C%3D6" alt="\left|x+1\right|=6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5" alt="x=5"/><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-1%3D6" alt="-x-1=6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3D7" alt="-x=7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-7" alt="x=-7"/><br/> <br/> <a href="https://peda.net/p/oskari.lahtinen/mag/1iji/116/sieppaa-png2#top" title="Sieppaa.PNG"><img src="https://peda.net/p/oskari.lahtinen/mag/1iji/116/sieppaa-png2:file/photo/7a212579cc9ccf3773af4cddafc32391e5956e10/Sieppaa.PNG" alt="" title="Sieppaa.PNG" class="inline" loading="lazy"/></a> 2019-08-15T10:50:42+03:00 https://peda.net/id/4337898abf3 2019-08-15T10:42:41+03:00 a) epätosi, itseisarvo on aina positiivinen tai nolla<br/> b) tosi<br/> c) epätosi, itseisarvo olisi negatiivinen jos a on negatiivinen luku<br/> d) tosi<br/> e) epätosi, myös silloin kun a=-13 2019-08-15T10:42:41+03:00 https://peda.net/id/6540aeeabf2 2019-08-15T11:13:36+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-a%5Cright%7C%2B%5Cleft%7Ca%5Cright%7C" alt="\left|-a\right|+\left|a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2a%5Cright%7C" alt="\left|2a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2%5Cleft%7Ca%5Cright%7C" alt="2\left|a\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-5a%5Cright%7C" alt="\left|-5a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C5a%5Cright%7C" alt="\left|5a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=5%5Cleft%7Ca%5Cright%7C" alt="5\left|a\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-2a%5Cright%7C-%5Cleft%7C-a%5Cright%7C" alt="\left|-2a\right|-\left|-a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2a%5Cright%7C-%5Cleft%7Ca%5Cright%7C" alt="\left|2a\right|-\left|a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca%5Cright%7C" alt="\left|a\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-a-b%5Cright%7C" alt="\left|-a-b\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-a%5Cright%7C%2B%5Cleft%7C-b%5Cright%7C" alt="\left|-a\right|+\left|-b\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca%5Cright%7C%2B%5Cleft%7Cb%5Cright%7C" alt="\left|a\right|+\left|b\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cb-a%5Cright%7C" alt="\left|b-a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-1%5Cleft(-b%2Ba%5Cright)%5Cright%7C" alt="\left|-1\left(-b+a\right)\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-1%5Cright%7C%5Cleft%7C-b%2Ba%5Cright%7C" alt="\left|-1\right|\left|-b+a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca-b%5Cright%7C" alt="\left|a-b\right|"/> 2019-08-15T10:36:29+03:00 https://peda.net/id/9262a776bf2 2019-08-15T10:30:35+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2a%5Cright%7C-%5Cleft%7C3a%5Cright%7C" alt="\left|2a\right|-\left|3a\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca%5Cright%7C" alt="\left|a\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-2a%5Cright%7C%2B%5Cleft%7C3a%5Cright%7C" alt="\left|-2a\right|+\left|3a\right|"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=5%5Cleft%7Ca%5Cright%7C" alt="5\left|a\right|"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca%5E2%2B1%5Cright%7C%2B%5Cleft%7Ca%5Cright%7C%5E2-%5Cleft%7C3a%5E2%5Cright%7C" alt="\left|a^2+1\right|+\left|a\right|^2-\left|3a^2\right|"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=1-a%5E2" alt="1-a^2"/></div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca-2%5Cright%7C%5E2" alt="\left|a-2\right|^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(a-2%5Cright)%5E2" alt="\left(a-2\right)^2"/></div> 2019-08-15T10:30:35+03:00 https://peda.net/id/076ab98ebdb 2019-08-13T14:10:59+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3x%5E2-7x%2B1%5Cright%7C%3D1%7B%2C%7D%5C%20x%3D0%5C%20" alt="\left|3x^2-7x+1\right|=1{,}\ x=0\ "/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-x%5E2%5Cright%7C-%5Cleft%7C3-x%5Cright%7C%3D0%7B%2C%7D%5C%20x%3D1" alt="\left|3-x^2\right|-\left|3-x\right|=0{,}\ x=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C5x-10%5Cright%7C%2B%5Cleft%7Cx%5E2-4%5Cright%7C%3D0%7B%2C%7D%5C%20x%3D-7%5C%20tai%5C%20x%3D2" alt="\left|5x-10\right|+\left|x^2-4\right|=0{,}\ x=-7\ tai\ x=2"/> 2019-08-13T14:10:59+03:00 https://peda.net/id/8dafb856bdb 2019-08-13T14:07:35+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C5x%2B3%5Cright%7C%3D%5Cleft%7C7-x%5Cright%7C%7B%2C%7D%5C%20x%3D%5Cfrac%7B2%7D%7B3%7D" alt="\left|5x+3\right|=\left|7-x\right|{,}\ x=\frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-x%5Cright%7C%3D%5Cleft%7Cx%2B9%5Cright%7C%7B%2C%7D%5C%20x%3D-3" alt="\left|3-x\right|=\left|x+9\right|{,}\ x=-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5E2-x%5Cright%7C%3D%5Cleft%7C1-x%5E2%5Cright%7C%7B%2C%7D%5C%20x%3D1" alt="\left|x^2-x\right|=\left|1-x^2\right|{,}\ x=1"/> 2019-08-13T14:07:35+03:00 https://peda.net/id/798dfc6cbdb 2019-08-13T13:59:51+03:00 a) yhtälöiden 2|x-3|=1 ja |2x-6|=1 ratkaisut ovat samat, koska |ab|=|a||b|<br/> <br/> b)<br/> 2|x-3|=1<br/> <br/> x=3,5<br/> <br/> <br/> 3|x-1|=4|x+2|<br/> |3x-3|=|4x+8|<br/> <br/> ratkaistaan symbolisen laskennan ohjelmalla<br/> x=-11 2019-08-13T13:59:51+03:00 https://peda.net/id/4aa32784bdb 2019-08-13T13:51:23+03:00 A 1<br/> B 3<br/> C 4<br/> D 2 2019-08-13T13:51:23+03:00 https://peda.net/id/a383fbeebdb 2019-08-13T13:18:05+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5E2-1%5Cright%7C%3D3%7B%2C%7D%5C%20x%3D%5Cpm2" alt="\left|x^2-1\right|=3{,}\ x=\pm2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5E2-x%2B2%5Cright%7C%3D4%7B%2C%7D%5C%20x%3D2" alt="\left|x^2-x+2\right|=4{,}\ x=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5E3%2B%5Cfrac%7B7%7D%7B16%7D%5Cright%7C%3D%5Cfrac%7B9%7D%7B16%7D%7B%2C%7D%5C%20x%3D%5Cfrac%7B1%7D%7B2%7D" alt="\left|x^3+\frac{7}{16}\right|=\frac{9}{16}{,}\ x=\frac{1}{2}"/> 2019-08-13T13:18:05+03:00 https://peda.net/id/3b056922bdb 2019-08-13T13:15:09+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-2x%5Cright%7C%3D11%7B%2C%7D%5C%20x%3D7" alt="\left|3-2x\right|=11{,}\ x=7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-2x%5Cright%7C%3D-2%7B%2C%7D%5C%20ei%5C%20ratkaisua" alt="\left|3-2x\right|=-2{,}\ ei\ ratkaisua"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-2x%5Cright%7C%3D0%7B%2C%7D%5C%20x%3D%5Cfrac%7B3%7D%7B2%7D" alt="\left|3-2x\right|=0{,}\ x=\frac{3}{2}"/> 2019-08-13T13:15:09+03:00 https://peda.net/id/f6c4055cbdb 2019-08-15T10:14:36+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2x-1%5Cright%7C-5%3D0" alt="\left|2x-1\right|-5=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2x-1%5Cright%7C%3D5" alt="\left|2x-1\right|=5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x-1%3D5" alt="2x-1=5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D6" alt="2x=6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><!--filtered attribute: style="display: inline;"--><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=2x-1%3D-5" alt="2x-1=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D-4" alt="2x=-4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-2" alt="x=-2"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3x%2B2%5Cright%7C%3D0%7B%2C%7D%5C%20x%3D-%5Cfrac%7B2%7D%7B3%7D" alt="\left|3x+2\right|=0{,}\ x=-\frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C7x-1%5Cright%7C%3D-2" alt="\left|7x-1\right|=-2"/>, ei ratkaisua, koska minkään luvun itseisarvo ei ole negatiivinen 2019-08-13T13:13:15+03:00 https://peda.net/id/3091a0b0bdb 2019-08-13T13:07:42+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3-%5Csqrt%7B10%7D%5Cright%7C%3D%5Csqrt%7B10%7D-3" alt="\left|3-\sqrt{10}\right|=\sqrt{10}-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5Cpi-3%5C%20%5Cfrac%7B1%7D%7B10%7D%5Cright%7C%3D%5Cpi-3%5C%20%5Cfrac%7B1%7D%7B10%7D" alt="\left|\pi-3\ \frac{1}{10}\right|=\pi-3\ \frac{1}{10}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Ca%5Cright%7C%3D-a%7B%2C%7D%5C%20kun%5C%20a%3C0" alt="\left|a\right|=-a{,}\ kun\ a&lt;0"/> 2019-08-13T13:07:42+03:00 https://peda.net/id/9e0aa264bdb 2019-08-13T13:03:36+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=-3-%5Cleft%7C-5%5Cright%7C%3D-8" alt="-3-\left|-5\right|=-8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-3-5%5Cright%7C%3D8" alt="\left|-3-5\right|=8"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C3%5Cright%7C-%5Cleft%7C5%5Cright%7C%3D-2" alt="\left|3\right|-\left|5\right|=-2"/> 2019-08-13T13:03:36+03:00 https://peda.net/id/29e4e890bdb 2019-08-13T13:00:22+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%2B3%5Cright%7C%3D4%7B%2C%7D%5C%20x%3D1%5C%20tai%5C%20x%3D-7" alt="\left|x+3\right|=4{,}\ x=1\ tai\ x=-7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C2x%2B1%5Cright%7C%3D7%7B%2C%7D%5C%20x%3D3%5C%20tai%5C%20x%3D-4" alt="\left|2x+1\right|=7{,}\ x=3\ tai\ x=-4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7Cx%5Cright%7C%3D0%7B%2C%7D%5C%20x%3D0" alt="\left|x\right|=0{,}\ x=0"/> 2019-08-13T13:00:22+03:00 https://peda.net/id/d732769ebdb 2019-08-13T12:58:03+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5C%203-%5Cpi%5Cright%7C%3D%5Cpi-3" alt="\left|\ 3-\pi\right|=\pi-3"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C1-%5Csqrt%7B2%7D%5Cright%7C%3D%5Csqrt%7B2%7D-1" alt="\left|1-\sqrt{2}\right|=\sqrt{2}-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C4-%5Csqrt%7B13%7D%5Cright%7C%3D%5Csqrt%7B13%7D-4" alt="\left|4-\sqrt{13}\right|=\sqrt{13}-4"/> 2019-08-13T12:58:03+03:00 https://peda.net/id/647dabb4bdb 2019-08-13T12:54:50+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=2%5E2%3E%5Cleft(%5Csqrt%7B3%7D%5Cright)%5E2" alt="2^2&gt;\left(\sqrt{3}\right)^2"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=4%3E3" alt="4&gt;3"/></div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C%5Csqrt%7B3%7D-2%5Cright%7C%3D2-%5Csqrt%7B3%7D" alt="\left|\sqrt{3}-2\right|=2-\sqrt{3}"/></div> 2019-08-13T12:54:50+03:00 https://peda.net/id/fc51c020bda 2019-08-13T12:51:56+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-4%5Cright%7C%3D4" alt="\left|-4\right|=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-%5Cfrac%7B2%7D%7B3%7D%5Cright%7C%3D%5Cfrac%7B2%7D%7B3%7D" alt="\left|-\frac{2}{3}\right|=\frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B3%7Dja%5C%20-%5Csqrt%7B3%7D" alt="\sqrt{3}ja\ -\sqrt{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=24%5C%20ja%5C%20-24" alt="24\ ja\ -24"/> 2019-08-13T12:51:56+03:00 https://peda.net/id/c33b19dabda 2019-08-13T12:50:20+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C7%5Cright%7C%3D7" alt="\left|7\right|=7"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-%5Cfrac%7B5%7D%7B8%7D%5Cright%7C%3D%5Cfrac%7B5%7D%7B8%7D" alt="\left|-\frac{5}{8}\right|=\frac{5}{8}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft%7C-%5Csqrt%7B13%7D%5Cright%7C%3D%5Csqrt%7B13%7D" alt="\left|-\sqrt{13}\right|=\sqrt{13}"/> 2019-08-13T12:50:20+03:00