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 50

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 :(a) 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 50

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 :(a) 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 50

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

-5 50

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

-5 50

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

-5 50

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 1.6Penyelesaian :

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 :

SEKIAN DAN

TERIMA KASIH