Pembahasan Soal Ujian Nasional Matematika SMP Part 7

Soal 13 (Persamaan Linear Satu Variabel)

Nilai x yang memenuhi

$\frac{1}{4}\left( {x - 8} \right) = 8 + \frac{2}{3}x$ adalah ....

A. -24

B. -12

C. 12

D. 24

Jawab:

$\begin{array}{l} \frac{1}{4}\left( {x - 8} \right) = 8 + \frac{2}{3}x \\ \Leftrightarrow \frac{1}{4}x - 2 = 8 + \frac{2}{3}x \\ \Leftrightarrow \frac{1}{4}x - \frac{2}{3}x = 8 + 2 \\ \Leftrightarrow \frac{3}{{12}}x - \frac{8}{{12}}x = 10 \\ \Leftrightarrow - \frac{5}{{12}}x = 10 \\ \Leftrightarrow x = - \frac{{12}}{5} \times 10 \\ \Leftrightarrow x = - 24 \\ \end{array}$

Jawaban yang benar adalah A.

Soal 14 (Himpunan)

Diketahui:

$\begin{array}{l} S = \left\{ {x|x \le 10,\begin{array}{*{20}{c}} x {bilangan} {cacah} \\ \end{array}} \right\} \\ K = \left\{ {x|x \le 8,\begin{array}{*{20}{c}} x {faktor} 8 \\ \end{array}} \right\} \\ L = \left\{ {x|1 \le x \le 10,\begin{array}{*{20}{c}} x {bilangan} {prima} \\ \end{array}} \right\} \\ {\left( {K - L} \right)^C} = \cdots \\ \end{array}$

A. {1, 4, 8}

B. {2, 3, 5, 7}

C. {1, 2, 3, 5, 6, 7, 9, 10}

D. {0, 2, 3, 5, 6, 7, 9, 10}

Jawab:

$\begin{array}{l} S = \left\{ {0,1,2,3,4,5,6,7,8,9,10} \right\} \\ K = \left\{ {1,2,4,8} \right\} \\ L = \left\{ {2,3,5,7} \right\} \\ {\left( {K - L} \right)^C} = {\left\{ {1,4,8} \right\}^C} \\ = \left\{ {0,2,3,5,6,7,9,10} \right\} \\ \end{array}$

Jawaban yang benar adalah D.