Contoh Soal Nilai Mutlak (Kelas X Matematika Wajib)

$\begin{array}{ll}\\ 1.&\textrm{Penyelesaian}\: \: -5\left |x-7 \right |+2=-13\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&x=-10\: \: \textrm{dan}\: \: x=-4\\ \textrm{b}.&x=-10\: \: \textrm{dan}\: \: x=-2\\ \textrm{c}.&x=-2\: \: \textrm{dan}\: \: x=4\\ \textrm{d}.&x=4\: \: \textrm{dan}\: \: x=-10\\ \color{red}\textrm{e}.&x=4\: \: \textrm{dan}\: \: x=10\end{array}\\\\ &\textrm{Jawab}:\quad \textbf{e}\\ &\begin{aligned}-5\left |x-7 \right |&=-13-2\\ \left |x-7 \right |&=\displaystyle \frac{-15}{-5}\\ \left |x-7 \right |&=3\\ x-7&=\pm 3\\ x&=\mp 3+7\\ x&=\begin{cases} +3 & \text{ + } 7=10 \\\\ -3 & \text{ + } 7=4 \end{cases} \end{aligned}\end{array}$

$\begin{array}{ll}\\ 2.&\textrm{Diketahui persamaan}\: \: \left |x-5 \right |+\left | x+9 \right |=22\\ &\textrm{dan diberikan pernyataan-pernyataan berikut}\\ &\textrm{untuk}\\ &(\textrm{i})\quad x<-9,\: \textrm{maka}\: \: -x+5-x+9=22\\ &(\textrm{ii})\: \: \: -9\leq x< 5,\: \textrm{maka}\: \: -x+5-x+9=22\\ &(\textrm{iii})\: \: x<-9,\: \textrm{maka}\: \: -x+5-x-9=22\\ &(\textrm{iv})\: \: \: x\geq 5,\: \textrm{maka}\: \: x-5+x+9=22\\ &\textrm{Pernyataan yang tepa ditunjukkan oleh}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&(\textrm{i})\: \: \textrm{dan}\: \: (\textrm{ii})\\ \textrm{b}.&(\textrm{i})\: \: \textrm{dan}\: \: (\textrm{iii})\\ \color{red}\textrm{c}.&(\textrm{i})\: \: \textrm{dan}\: \: (\textrm{iv})\\ \textrm{d}.&(\textrm{ii})\: \: \textrm{dan}\: \: (\textrm{iii})\\ \textrm{e}.&(\textrm{iii})\: \: \textrm{dan}\: \: (\textrm{iv}) \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\begin{aligned} \end{aligned}\end{array}$

$\begin{array}{l}\\ 3.&\textrm{Nilai}\: \: x\: \: \textrm{yang memenuhi persamaan}\\ &3\left |x-1 \right |-2\left | x+1 \right |=0\\ &\textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&x=-\displaystyle \frac{1}{5}\: \: \textrm{dan}\: \: x=5\\ \textrm{b}.&x=-5\: \: \textrm{dan}\: \: x=-\displaystyle \frac{1}{5}\\ \color{red}\textrm{c}.&\displaystyle x=\frac{1}{5}\: \: \textrm{dan}\: \: x=5\\\\ \textrm{d}.&x=-5\: \: \textrm{dan}\: \: x=\displaystyle \frac{1}{5}\\\\ \textrm{e}.&x=-5\: \: \textrm{dan}\: \: x=5\\ \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\begin{aligned}3\left |x-1 \right |&-2\left | x+1 \right |=0 \\ 3\left |x-1 \right |&=2\left | x+1 \right |\\ 3^{2}(x-1)^{2}&=2^{2}(x+1)^{2}\\ 9\left ( x^{2}-2x+1 \right )&=4\left ( x^{2}+2x+1 \right )\\ 9x^{2}-4x^{2}&-18x-8x+9-4=0\\ 5x^{2}-26x&+5=0\\ (5x-1)&(x-5)=0\\ x=\displaystyle \frac{1}{5}\quad &\textrm{atau}\quad x=5 \end{aligned} \end{array}$

$\begin{array}{l}\\ 4.&\textrm{Himpunan penyelesaian dari}\: \: \left | 5-\displaystyle \frac{2}{3}x \right |-9=8\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&\left \{ -33,-18 \right \}\\ \color{red}\textrm{b}.&\left \{ -18,33 \right \}\\ \textrm{c}.&\left \{ 33,8 \right \}\\ \textrm{d}.&\left \{ 8,-33 \right \}\\ \textrm{e}.&\left \{ -8,33 \right \} \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{b}\\ &\color{blue}\begin{aligned}\left | 5-\displaystyle \frac{2}{3}x \right |&-9=8\\ \left | 5-\displaystyle \frac{2}{3}x \right |&=8+9=17\\ 5-\displaystyle \frac{2}{3}x&=\pm 17\\ -\displaystyle \frac{2}{3}x&=\pm 17-5\\ x&=\displaystyle \frac{\pm 17-5}{\left ( -\displaystyle \frac{2}{3} \right )}\\ x_{1}&=\displaystyle \left (\frac{17-5}{-2} \right )\times 3\\ &=-18\\ x_{2}&=\displaystyle \left (\frac{-17-5}{-2} \right )\times 3\\ &=33 \end{aligned} \end{array}$

$\begin{array}{ll}\\ 5.&\textrm{Harga buku di toko "KITA" adalah}\: \: 28.000,-\\ &\textrm{Jika harga buku tulis di toko "FAMILI" memiliki selisih}\: \: 7.000,-\\ &\textrm{Harga buku tulis di toko "FAMILI" dapat dinyatakan dengan}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&\left | x-7000 \right |=28000\\ \textrm{b}.&\left | x+7000 \right |=28000\\ \color{red}\textrm{c}.&\left | x-28000 \right |=7000\\ \textrm{d}.&\left | x+28000 \right |=7000\\ \textrm{e}.&\left | x-21000 \right |=7000\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ \end{array}$