Contoh Soal Lanjutan 2 Nilai Mutlak

$\begin{array}{l}\\ 11.&\textrm{Nilai}\: \: p\: \: \textrm{yang memenuhi}\: \: 10-4\left | 4-5p \right |=26\: \: \textrm{adalah... .}\\ &\begin{array}{lllllll}\\ \textrm{a}.&2\: \: \textrm{atau}\: \: 1\displaystyle \frac{2}{3}\\ \textrm{b}.&1\: \: \textrm{atau}\: \: -\displaystyle \frac{3}{5}\\\\ \textrm{c}.&2\: \: \textrm{atau}\: \: 2\displaystyle \frac{3}{5}\\ \textrm{d}.&-2\displaystyle \frac{3}{4}\: \: \textrm{atau}\: \: 1\\ \color{red}\textrm{e}.&-1\: \: \textrm{atau}\: \: 2\displaystyle \frac{3}{5}\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\color{blue}\begin{aligned}10-4\left | 4-5p \right |&=-26\\ -4\left | 4-5p \right |&=-36\\ \left | 4-5p \right |&=9\\ (4-5p)&=\pm 9\\ -5p&=-4\pm 9\\ p&=\displaystyle \frac{-4\pm 9}{-5}\\ p&=\begin{cases} \displaystyle \frac{-4+9}{-5} & =-1 \\ \textrm{atau} & \\ \displaystyle \frac{-4-9}{-5} & = \displaystyle \frac{13}{5}=2\frac{3}{5} \end{cases} \end{aligned} \end{array}$

$\begin{array}{l}\\ 12.&\textrm{Jika}\: \: 3<x<5\: \: \textrm{maka penyelesaian untuk}\\ &\sqrt{x^{2}-6x+9}-\sqrt{x^{2}-10x+25}=...\\ &\begin{array}{lllllll}\\ \textrm{a}.&2x-2\\ \textrm{b}.&2\\ \textrm{c}.&8-2x\\ \textrm{d}.&-2\\ \color{red}\textrm{e}.&2x-8\\ \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textbf{e}\\ &\color{blue}\begin{aligned}\sqrt{x^{2}-6x+9}&-\sqrt{x^{2}-10x+25}\\ &\sqrt{(x-3)^{2}}-\sqrt{(x-5)^{2}}\\ &=\left | x-3 \right |-\left | x-5 \right |\\ &\textrm{ingat bahwa saat}\\ \: \: 3<x<5\: \: &\textrm{maka}\\ &\: \begin{cases} \left | x-3 \right |=(x-3) \\ \left | x-5 \right |=-(x-5) \end{cases},\\ &\textrm{sehingga}\\ &=\left | x-3 \right |-\left | x-5 \right |\\ &=(x-3)-\left ( -(x-5) \right )\\ &=x-3+x-5\\ &=2x-8 \end{aligned} \end{array}$

$\begin{array}{l}\\ 13.&\textrm{Jika}\: \: 1<x<5\: \: \textrm{maka penyelesaian untuk}\\ &\sqrt{x^{2}-2x+1}+\sqrt{x^{2}-10x+25}=...\\ &\begin{array}{lllllll}\\ \textrm{a}.&2\\ \textrm{b}.&3\\ \color{red}\textrm{c}.&4\\ \textrm{d}.&5\\ \textrm{e}.&6\\ \end{array}\\\\ &\textbf{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}\sqrt{x^{2}-2x+1}&+\sqrt{x^{2}-10x+25}\\ &=\sqrt{(x-1)^{2}}+\sqrt{(x-5)^{2}}\\ &=\left | x-1 \right |+\left | x-5 \right |\\ &\textrm{ingat bahwa saat}\\ 1<x<5\: \: &\textrm{maka}\: \begin{cases} \left | x-1 \right |=(x-1) \\ \left | x-5 \right |=-(x-5) \end{cases},\\ & \textrm{sehingga}\\ &=\left | x-1 \right |+\left | x-5 \right |\\ &=(x-1)+\left ( -(x-5) \right )\\ &=x-1+5-x\\ &=4 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 14.&\textrm{Perhatikanlah ilustrasi grafik di bawah ini}\\ &\begin{aligned}\end{aligned}\end{array}$

$\begin{array}{l}\\ .\: \: \: \: \: \: &\textrm{Persamaan yang memenuhi rumus tersebut adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&y=\left | -x-2 \right |\\ \textrm{b}.&y=-2x-4\\ \textrm{c}.&y=-\left | 2x-4 \right |\\ \textrm{d}.&y=\left | -2x-4 \right |\\ \color{red}\textrm{e}.&y=\left | -2x+4 \right | \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\color{blue}\begin{aligned}&\textrm{Dengan cara substitusi langsung}\\ & \textrm{kita akan mendapatkan}\\ &\bullet \quad \textrm{untuk}\: \: x=4\: \: \textrm{menyebabkan nilai}\: \: y=4,\\ &\qquad\textrm{maka sampai langkah di sini hanya }\\ &\qquad\textrm{ada 1 persamaan yang memenuhi}\\ &\qquad\textrm{yaitu}:\: \: y=\left | -2x+4 \right | \end{aligned} \end{array}$

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

$\color{blue}\begin{aligned}&\qquad\textrm{berikut gambar grafiknya} \end{aligned}$