Contoh Soal Lanjutan 3 Nilai Mutlak

$\begin{array}{l}\\ 16.& \text{Penyelesaian dari}|3x-(4x-7)|=6\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& \{-1,-13\}\\ \text{b}.& \{-1,13\}\\ \text{c}.& \{1,13\}\\ \text{d}.& \{-13,1\}\\ \text{e}.& \left\{13\right\}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}|3x-(4x-7)|& =6\\ |3x-4x+7|& =6\\ |-x+7|& =6\\ (-x+7)& =\pm 6\\ -x& =\pm 6-7\\ \text{dikalikan}& \text{dengan}-1\\ x& =\pm 6+7\\ x_1& =+6+7=+13\\ x_2& =-6+7=+1\end{array}\end{array}$

$\begin{array}{l}\\ 17.& \text{Penyelesaian}|x-1|=2x+1\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& \{-2\}\\ \text{b}.& \{-2,0\}\\ \text{c}.& \{-1\}\\ \text{d}.& \left\{\right\}\\ \text{e}.& \left\{0\right\}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}|x-1|& =2x+1\\ (x-1)& =\pm (2x+1)\\ \text{untuk}& \{\begin{array}{ll}x\ge 1& \text{ maka }(x-1)=2x+1\\ x<1& \text{ maka }(x-1)=-(2x+1)\end{array}\\ & \begin{array}{|cc|}\hline x\ge 1& x<1\\ \begin{array}{rl}x-1& =2x+1\\ x-2x& =1+1\\ -x& =2\\ x& =-2\\ & \end{array}& \begin{array}{rl}x-1& =-(2x+1)\\ x-1& =-2x-1\\ x+2x& =-1+1\\ 3x& =0\\ x& =0\end{array}\\ \text{Tidak memenuhi}& \text{memenuhi}\\ \hline\end{array}\end{array}\end{array}$

$\begin{array}{l}\\ 18.& \text{Penyelesaian}|3a+1|=2a+9\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& \{-2\}\\ \text{b}.& \left\{8\right\}\\ \text{c}.& \{-2,8\}\\ \text{d}.& \left\{\right\}\\ \text{e}.& \text{Semua bilangan riil}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}|3a+1|& =2a+9\\ (3a+1)& =\pm (2a+9)\\ \text{untuk}& \{\begin{array}{ll}a\ge -{\displaystyle \frac{1}{3}}& \text{ maka }(3a+1)=2a+9\\ \\ a<-{\displaystyle \frac{1}{3}}& \text{ maka }(3a+1)=-(2a+9)\end{array}\\ & \begin{array}{|cc|}\hline a\ge {\displaystyle -\frac{1}{3}}& a<-{\displaystyle \frac{1}{3}}\\ \begin{array}{rl}3a+1& =2a+9\\ 3a-2a& =9-1\\ a& =8\\ & \\ & \\ & \\ & \end{array}& \begin{array}{rl}3a+1& =-(2a+9)\\ 3a+1& =-2a-9\\ 3a+2a& =-9-1\\ 5a& =-10\\ a& ={\displaystyle \frac{-10}{5}}\\ a& =-2\end{array}\\ \text{memenuhi}& \text{memenuhi}\\ \hline\end{array}\end{array}\end{array}$

$\begin{array}{l}\\ 19.& \text{Penyelesaian dari}|3x+2|=4x+5\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& -3\\ \text{b}.& -1\\ \text{c}.& -3\text{dan}-1\\ \text{d}.& \left\{\right\}\\ \text{e}.& 0\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{r}\begin{array}{rl}|3x+2|& =4x+5\\ (3x+2)& =\pm (4x+5)\\ \text{untuk}& \{\begin{array}{ll}x\ge -{\displaystyle \frac{2}{3}}& \text{ maka }3x+2=4x+5\\ \\ x<-{\displaystyle \frac{2}{3}}& \text{ maka }3x+2=-(4x+5)\end{array}\\ & \begin{array}{|cc|}\hline x\ge -{\displaystyle \frac{2}{3}}& x<-{\displaystyle \frac{2}{3}}\\ \begin{array}{rl}3x+2& =4x+5\\ 3x-4x& =5-2\\ -& =3\\ x& =-3\\ & \\ & \end{array}& \begin{array}{rl}3x+2& =-(4x+5)\\ 3x+2& =-4x-5\\ 3x+4x& =-5-2\\ 7x& =-7\\ x& ={\displaystyle \frac{-7}{7}}\\ x& =-1\end{array}\\ \hline\end{array}\end{array}\end{array}\end{array}$

$\begin{array}{l}\\ 20.& \text{Jika}|-3x|+4y^{-1}=6z+4x,\\ & \text{maka nilai}x\text{dinyatakan dalam}y\text{dan}z\text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& {\displaystyle \frac{y}{4}-6z}\\ \text{b}.& {\displaystyle \frac{4}{y}-6z}\\ \text{c}.& 4-{\displaystyle \frac{6}{y}}\\ \text{d}.& {\displaystyle \frac{4}{7y}+\frac{6z}{7}}\\ \text{e}.& {\displaystyle \frac{7}{4y}+6z}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}|-3x|& +4y^{-1}=6z+4x\\ |-3x|& =6z+4x-4y^{-1}\\ -3x& =\pm (6z+4x-4y^{-1})\\ \text{untuk}& :x\ge 0\\ -3x& =6z+4x-4y^{-1}\\ -3x-4x& =6z-4y^{-1}\\ -7x& =6z-4y^{-1}\\ x& ={\displaystyle \frac{6z-4y^{-1}}{-7}}\\ & =\frac{4}{7y}-\frac{6z}{7}\\ untuk& :x<0\\ -3x& =-(6z+4x-4y^{-1})\\ -3x& =-6z-4x+4y^{-1}\\ -3x+4x& =-6z+4y^{-1}\\ x& =4y^{-1}-6z\\ & ={\displaystyle \frac{4}{y}-6z}\end{array}\end{array}$