Contoh Soal Lanjutan 2 Nilai Mutlak

$\begin{array}{l}\\ 11.& \text{Nilai}p\text{yang memenuhi}10-4|4-5p|=26\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& 2\text{atau}1{\displaystyle \frac{2}{3}}\\ \text{b}.& 1\text{atau}-{\displaystyle \frac{3}{5}}\\ \\ \text{c}.& 2\text{atau}2{\displaystyle \frac{3}{5}}\\ \text{d}.& -2{\displaystyle \frac{3}{4}\text{atau}1}\\ \text{e}.& -1\text{atau}2{\displaystyle \frac{3}{5}}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}10-4|4-5p|& =-26\\ -4|4-5p|& =-36\\ |4-5p|& =9\\ (4-5p)& =\pm 9\\ -5p& =-4\pm 9\\ p& ={\displaystyle \frac{-4\pm 9}{-5}}\\ p& =\{\begin{array}{ll}{\displaystyle \frac{-4+9}{-5}}& =-1\\ \text{atau}& \\ {\displaystyle \frac{-4-9}{-5}}& ={\displaystyle \frac{13}{5}=2\frac{3}{5}}\end{array}\end{array}\end{array}$

$\begin{array}{l}\\ 12.& \text{Jika}3<x<5\text{maka penyelesaian untuk}\\ & \sqrt{x^2-6x+9}-\sqrt{x^2-10x+25}=...\\ & \begin{array}{l}\\ \text{a}.& 2x-2\\ \text{b}.& 2\\ \text{c}.& 8-2x\\ \text{d}.& -2\\ \text{e}.& 2x-8\end{array}\\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{e}}\\ & \begin{array}{rl}\sqrt{x^2-6x+9}& -\sqrt{x^2-10x+25}\\ & \sqrt{(x-3{)}^2}-\sqrt{(x-5{)}^2}\\ & =|x-3|-|x-5|\\ & \text{ingat bahwa saat}\\ 3<x<5& \text{maka}\\ & \{\begin{array}{l}|x-3|=(x-3)\\ |x-5|=-(x-5)\end{array},\\ & \text{sehingga}\\ & =|x-3|-|x-5|\\ & =(x-3)-(-(x-5))\\ & =x-3+x-5\\ & =2x-8\end{array}\end{array}$

$\begin{array}{l}\\ 13.& \text{Jika}1<x<5\text{maka penyelesaian untuk}\\ & \sqrt{x^2-2x+1}+\sqrt{x^2-10x+25}=...\\ & \begin{array}{l}\\ \text{a}.& 2\\ \text{b}.& 3\\ \text{c}.& 4\\ \text{d}.& 5\\ \text{e}.& 6\end{array}\\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{c}}\\ & \begin{array}{rl}\sqrt{x^2-2x+1}& +\sqrt{x^2-10x+25}\\ & =\sqrt{(x-1{)}^2}+\sqrt{(x-5{)}^2}\\ & =|x-1|+|x-5|\\ & \text{ingat bahwa saat}\\ 1<x<5& \text{maka}\{\begin{array}{l}|x-1|=(x-1)\\ |x-5|=-(x-5)\end{array},\\ & \text{sehingga}\\ & =|x-1|+|x-5|\\ & =(x-1)+(-(x-5))\\ & =x-1+5-x\\ & =4\end{array}\end{array}$

$\begin{array}{l}\\ 14.& \text{Perhatikanlah ilustrasi grafik di bawah ini}\\ & \begin{array}{}\end{array}\end{array}$

$\begin{array}{l}\\ .& \text{Persamaan yang memenuhi rumus tersebut adalah... .}\\ & \begin{array}{l}\\ \text{a}.& y=|-x-2|\\ \text{b}.& y=-2x-4\\ \text{c}.& y=-|2x-4|\\ \text{d}.& y=|-2x-4|\\ \text{e}.& y=|-2x+4|\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}& \text{Dengan cara substitusi langsung}\\ & \text{kita akan mendapatkan}\\ & \bullet \text{untuk}x=4\text{menyebabkan nilai}y=4,\\ & \text{maka sampai langkah di sini hanya }\\ & \text{ada 1 persamaan yang memenuhi}\\ & \text{yaitu}:y=|-2x+4|\end{array}\end{array}$

$\begin{array}{l}\\ 15.& \text{Gambarlah garfik untuk persamaan}\left|x\right|+\left|y\right|=4\\ \\ \\ & \text{Jawab}:\\ \\ & \text{untuk}\left|x\right|+\left|y\right|=4\\ \\ & \begin{array}{|cccc|}\hline x>0,y>0& & & x>0,y<0\\ x+y=4& & & x+(-y)=4\\ & & & \\ & & & \\ x<0,y>0& & & x<0,y<0\\ (-x)+y=4& & & (-x)+(-y)=4\\ \hline\end{array}\end{array}$

$\begin{array}{rl}& \text{berikut gambar grafiknya}\end{array}$