LATIHAN SOAL & PENYELESAIANNYA (Persamaan dan Pertidaksamaan di Ruang Satu dengan Satu Variabel) Disusun oleh : KARLINA SARI (4101412031) ALIFA MUHANDIS S A (4101412084) RIA WINARTI NINGRUM (4101412180) TASBIATUN (4101412 )

1. Graph each set of number and write each set as the intersection or union of two sets. {x|x < -4 or x ≥ 4} Penyelesaian : Gambar grafik -5 5

Point having coordinates between -2 and 2, together with poins 2. (a) Graph each set of points. (b) express set of numbers using set- builder notation and interval notation. Point having coordinates between -2 and 2, together with poins with coordinates greater than 5. Penyelesaian : Gambar grafik (b) Set builder notation {x|-2 ˂ x ˂ 2 and x ˃ 5} = {x |-2 ˂ x < 2} U {x|x > 5} interval notation (-2,2) U (5,+~) -5 5

(b) Set builder notation 3. (a) Graph each set of points. (b) express set of numbers using set-builder notation and interval notation. Point having coordinates less than -4, together with poins coordinates beetwen 0 and 4. Penyelesaian : Gambar grafik (b) Set builder notation {x|x ˂ -4 and 0 < x < 4} = {x |x < -4} U {x|0 < x < 4} interval notation (-~,-4) U (0,4) -5 5

4. Write an equivalent pair of inequalities without using absolute value notation, solve, and graph the solution set. | x－1 | ≤ 2 Is equivalent to -2 ≤ x－1 ≤ 2 Penyelesaian : Gambar Grafik: -2 ≤ x－1 ≤ 2 -1 ≤ x ≤ 3 -5 5

5. Write an equivalent pair of inequalities without using absolute value notation, solve, and graph the solution set. |2x－3| ≤ 5 Is equivalent to -5 ≤ 2x－3 ≤ 5 Penyelesaian : Gambar Grafik : -5 ≤ 2x-3 ≤ 5 -2 ≤ 2x ≤ 8 -1 ≤ x ≤ 4 -5 5

6. Write an equivalent pair of inequalities without using absolute value notation, solve, and graph the solution set. |3x + 2| ≤ 6 Is equivalent to -6 ≤ 3x + 2 ≤ 6 Penyelesaian : Gambar Grafik : -6 ≤ 3x + 2 ≤ 6 -8 ≤ 3x ≤ 4 -5 5

7. Express each of the following as a single inequality using absolute value notation -5 ≤ 2x － 1 ≤ 5 Is equivalent to | 2x － 1 | ≤ 5

8. Pembuktian teorema 1.6 Penyelesaian : If and are the endpoint of a segment and the point separates the segment into two parts length and then and where            

  Menggunakan kesebangunan : = = = k = = k = dikalikan ( k ( = x ( k ( () dijumlahkan dengan k ( + = k (

9. Show that the two line segments whose endpoints are (8,-5), (5,7) and (0,-7), (8,-5) are perpendicular. Penyelesaian : Titik (8,-5) dan (5,7) mempunyai gradien -4 sedangkan titik 90,-7) dan (8,-5) mempunyai gradien ¼ maka dua ruas garis tersebut tegak lurus karena hasil kali dua gradiennya -1

10. Graph each interval (-3,4) Penyelesaian : interval dari (-3,4) adalah -3 < x < 4

11. Show that the midpoint of the hypotenusa of a right triangle equidistant the vertices of the triangle. Hint : set vertex of right angle at (0,0) and the other vertices at (a,0) and (0,b). Penyelesaian :

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