Contoh Soal Lanjutan 3 Nilai Mutlak

$\begin{array}{l}\\ 16.&\textrm{Penyelesaian dari}\: \: \left | 3x-(4x-7) \right |=6\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&\left \{ -1,-13 \right \}\\ \textrm{b}.&\left \{ -1,13 \right \}\\ \color{red}\textrm{c}.&\left \{ 1,13 \right \}\\ \textrm{d}.&\left \{ -13,1 \right \}\\ \textrm{e}.&\left \{ 13 \right \} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}\left | 3x-(4x-7) \right |&=6\\ \left | 3x-4x+7 \right |&=6\\ \left | -x+7 \right |&=6\\ (-x+7)&=\pm 6\\ -x&=\pm 6-7\\ \textrm{dikalikan}\: \: & \textrm{dengan}\: \: \color{black}-1\\ x&=\pm 6+7\\ x_{1}&=+6+7=+13\\ x_{2}&=-6+7=+1 \end{aligned} \end{array}$

$\begin{array}{l}\\ 17.&\textrm{Penyelesaian}\: \: \left | x-1 \right |=2x+1\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&\left \{ -2 \right \}\\ \textrm{b}.&\left \{ -2,0 \right \}\\ \textrm{c}.&\left \{ -1 \right \}\\ \textrm{d}.&\left \{ \: \: \, \right \}\\ \color{red}\textrm{e}.&\left \{ 0 \right \} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\color{blue}\begin{aligned}\left | x-1 \right |&=2x+1\\ (x-1)&=\pm (2x+1)\\ \textrm{untuk}\: &\begin{cases} x\geq 1 & \text{ maka } (x-1)=2x+1 \\ x< 1 & \text{ maka } (x-1)=-(2x+1) \end{cases}\\ &\begin{array}{|c|c|}\hline x\geq 1&x< 1\\\hline \begin{aligned}x-1&=2x+1\\ x-2x&=1+1\\ -x&=2\\ x&=-2\\ & \end{aligned}&\begin{aligned}x-1&=-(2x+1)\\ x-1&=-2x-1\\ x+2x&=-1+1\\ 3x&=0\\ x&=0 \end{aligned}\\\hline \textrm{Tidak memenuhi}&\textrm{memenuhi}\\\hline \end{array} \end{aligned} \end{array}$

$\begin{array}{l}\\ 18.&\textrm{Penyelesaian}\: \: \left | 3a+1 \right |=2a+9\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&\left \{ -2 \right \}\\ \textrm{b}.&\left \{ 8 \right \}\\ \color{red}\textrm{c}.&\left \{ -2,8 \right \}\\ \textrm{d}.&\left \{ \: \: \, \right \}\\ \textrm{e}.&\textrm{Semua bilangan riil} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}\left | 3a+1 \right |&=2a+9\\ (3a+1)&=\pm (2a+9)\\ \textrm{untuk}\: &\begin{cases} a\geq -\displaystyle \frac{1}{3} & \text{ maka } (3a+1)=2a+9 \\\\ a< -\displaystyle \frac{1}{3} & \text{ maka } (3a+1)=-(2a+9) \end{cases}\\ &\begin{array}{|c|c|}\hline a\geq \displaystyle -\frac{1}{3}&a< -\displaystyle \frac{1}{3}\\\hline \begin{aligned}3a+1&=2a+9\\ 3a-2a&=9-1\\ a&=8\\ &\\ &\\ &\\ & \end{aligned}&\begin{aligned}3a+1&=-(2a+9)\\ 3a+1&=-2a-9\\ 3a+2a&=-9-1\\ 5a&=-10\\ a&=\displaystyle \frac{-10}{5}\\ a&=-2 \end{aligned}\\\hline \textrm{memenuhi}&\textrm{memenuhi}\\\hline \end{array} \end{aligned} \end{array}$

$\begin{array}{l}\\ 19.&\textrm{Penyelesaian dari}\: \: \left | 3x+2 \right |=4x+5\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&-3\\ \color{red}\textrm{b}.&-1\\ \textrm{c}.&-3\: \: \textrm{dan}\: \: -1\\ \textrm{d}.&\left \{ \: \:  \right \} \\ \textrm{e}.&0 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\begin{aligned}\color{blue}\begin{aligned}\left | 3x+2 \right |&=4x+5\\ (3x+2)&=\pm (4x+5)\\ \textrm{untuk}\: &\begin{cases} x\geq -\displaystyle \frac{2}{3} & \text{ maka } 3x+2=4x+5 \\\\ x< -\displaystyle \frac{2}{3} & \text{ maka } 3x+2=-(4x+5) \end{cases}\\ &\begin{array}{|c|c|}\hline x\geq -\displaystyle \frac{2}{3}&x< -\displaystyle \frac{2}{3}\\\hline \begin{aligned}3x+2&=4x+5\\ 3x-4x&=5-2\\ -&=3\\ x&=-3\\ &\\ & \end{aligned}&\begin{aligned}3x+2&=-(4x+5)\\ 3x+2&=-4x-5\\ 3x+4x&=-5-2\\ 7x&=-7\\ x&=\displaystyle \frac{-7}{7}\\ x&=-1 \end{aligned}\\\hline \end{array} \end{aligned} \end{aligned} \end{array}$

$\begin{array}{l}\\ 20.&\textrm{Jika}\: \: \left | -3x \right |+4y^{-1}=6z+4x,\\ &\textrm{maka nilai}\: \: x\: \: \textrm{dinyatakan dalam}\: \: \: y\: \: \textrm{dan}\: \: z\: \: \textrm{adalah}....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{y}{4}-6z\\ \color{red}\textrm{b}.&\displaystyle \frac{4}{y}-6z\\ \textrm{c}.&4-\displaystyle \frac{6}{y}\\ \textrm{d}.&\displaystyle \frac{4}{7y}+\frac{6z}{7}\\ \textrm{e}.&\displaystyle \frac{7}{4y}+6z \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}\left | -3x \right |&+4y^{-1}=6z+4x\\ \left | -3x \right |&=6z+4x-4y^{-1}\\ -3x&=\pm (6z+4x-4y^{-1})\\ \textrm{untuk}&:\: x\geq 0\\ -3x&=6z+4x-4y^{-1}\\ -3x-4x&=6z-4y^{-1}\\ -7x&=6z-4y^{-1}\\ x&=\displaystyle \frac{6z-4y^{-1}}{-7}\\ &=\frac{4}{7y}-\frac{6z}{7}\\ untuk&:\: x<0\\ -3x&=-(6z+4x-4y^{-1})\\ -3x&=-6z-4x+4y^{-1}\\ -3x+4x&=-6z+4y^{-1}\\ x&=4y^{-1}-6z\\ &=\displaystyle \frac{4}{y}-6z \end{aligned} \end{array}$