Contoh Soal Nilai Mutlak (Kelas X Matematika Wajib)

$\begin{array}{l}\\ 1.& \text{Penyelesaian}-5|x-7|+2=-13\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& x=-10\text{dan}x=-4\\ \text{b}.& x=-10\text{dan}x=-2\\ \text{c}.& x=-2\text{dan}x=4\\ \text{d}.& x=4\text{dan}x=-10\\ \text{e}.& x=4\text{dan}x=10\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}-5|x-7|& =-13-2\\ |x-7|& ={\displaystyle \frac{-15}{-5}}\\ |x-7|& =3\\ x-7& =\pm 3\\ x& =\mp 3+7\\ x& =\{\begin{array}{ll}+3& \text{ + }7=10\\ \\ -3& \text{ + }7=4\end{array}\end{array}\end{array}$

$\begin{array}{l}\\ 2.& \text{Diketahui persamaan}|x-5|+|x+9|=22\\ & \text{dan diberikan pernyataan-pernyataan berikut}\\ & \text{untuk}\\ & (\text{i})x<-9,\text{maka}-x+5-x+9=22\\ & (\text{ii})-9\le x<5,\text{maka}-x+5-x+9=22\\ & (\text{iii})x<-9,\text{maka}-x+5-x-9=22\\ & (\text{iv})x\ge 5,\text{maka}x-5+x+9=22\\ & \text{Pernyataan yang tepa ditunjukkan oleh}....\\ & \begin{array}{l}\\ \text{a}.& (\text{i})\text{dan}(\text{ii})\\ \text{b}.& (\text{i})\text{dan}(\text{iii})\\ \text{c}.& (\text{i})\text{dan}(\text{iv})\\ \text{d}.& (\text{ii})\text{dan}(\text{iii})\\ \text{e}.& (\text{iii})\text{dan}(\text{iv})\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{}\end{array}\end{array}$

$\begin{array}{l}\\ 3.& \text{Nilai}x\text{yang memenuhi persamaan}\\ & 3|x-1|-2|x+1|=0\\ & \text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& x=-{\displaystyle \frac{1}{5}\text{dan}x=5}\\ \text{b}.& x=-5\text{dan}x=-{\displaystyle \frac{1}{5}}\\ \text{c}.& {\displaystyle x=\frac{1}{5}\text{dan}x=5}\\ \\ \text{d}.& x=-5\text{dan}x={\displaystyle \frac{1}{5}}\\ \\ \text{e}.& x=-5\text{dan}x=5\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}3|x-1|& -2|x+1|=0\\ 3|x-1|& =2|x+1|\\ 3^2(x-1{)}^2& =2^2(x+1{)}^2\\ 9(x^2-2x+1)& =4(x^2+2x+1)\\ 9x^2-4x^2& -18x-8x+9-4=0\\ 5x^2-26x& +5=0\\ (5x-1)& (x-5)=0\\ x={\displaystyle \frac{1}{5}}& \text{atau}x=5\end{array}\end{array}$

$\begin{array}{l}\\ 4.& \text{Himpunan penyelesaian dari}|5-{\displaystyle \frac{2}{3}x}|-9=8\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& \{-33,-18\}\\ \text{b}.& \{-18,33\}\\ \text{c}.& \{33,8\}\\ \text{d}.& \{8,-33\}\\ \text{e}.& \{-8,33\}\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{b}}\\ & \begin{array}{rl}|5-{\displaystyle \frac{2}{3}x}|& -9=8\\ |5-{\displaystyle \frac{2}{3}x}|& =8+9=17\\ 5-{\displaystyle \frac{2}{3}x}& =\pm 17\\ -{\displaystyle \frac{2}{3}x}& =\pm 17-5\\ x& ={\displaystyle \frac{\pm 17-5}{(-{\displaystyle \frac{2}{3}})}}\\ x_1& ={\displaystyle \left(\frac{17-5}{-2}\right)\times 3}\\ & =-18\\ x_2& ={\displaystyle \left(\frac{-17-5}{-2}\right)\times 3}\\ & =33\end{array}\end{array}$

$\begin{array}{l}\\ 5.& \text{Harga buku di toko "KITA" adalah}28.000,-\\ & \text{Jika harga buku tulis di toko "FAMILI" memiliki selisih}7.000,-\\ & \text{Harga buku tulis di toko "FAMILI" dapat dinyatakan dengan}....\\ & \begin{array}{l}\\ \text{a}.& |x-7000|=28000\\ \text{b}.& |x+7000|=28000\\ \text{c}.& |x-28000|=7000\\ \text{d}.& |x+28000|=7000\\ \text{e}.& |x-21000|=7000\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\end{array}$