Question

Tolong di bantu jawab ya tolong pakek rumus​

Answer 1

1. Diketahui:

Ditanyakan:

Jawab:

Maka,

(B)

2. Diketahui:

-5 < 4x + 3 < 7

Ditanyakan:

x

Jawab:

-5 < 4x + 3 < 7

-5 - 3 < 4x + 3 - 3 < 7 - 3

-8 < 4x < 4

-8/4 < 4x/4 < 4/4

-2 < x < 1

(E)

3. Diketahui:

|5x-15| = 10

Ditanyakan:

x

Jawab:

|5x-15| = 10

|5x-15|² = 10²

25x²-150x+225 = 100

x²-6x+9 = 4

x²-6x+9-4 = 0

x²-6x+5 = 0

(x-5)(x-1) = 0

x = 5 atau x = 1 (E)

4. Diketahui:

|3x-7| = |2x+5|

Ditanyakan:

x

Jawab:

|3x-7|² = |2x+5|²

9x²-42x+49 = 4x²+20x+25

9x²-42x+49-4x²-20x-25 = 0

5x²-62x+24 = 0

5x²-60x-2x+24 = 0

5x(x-12)-2(x-12) = 0

(5x-2)(x-12) = 0

x= 2/5 atau x=12

(D)

5. Diketahui:

f(x) = |3x-9|

Ditanyakan:

f(2)

Jawab:

f(2) = |3(2)-9|

= |6-9|

= |-3|

= 3

(E)

6. Diketahui:

|x-2|+|2x+1| = 3

Ditanyakan:

x

Jawab:

|x-2|+|2x+1| = 3

* |x-2| =

• x-2 jika x-2 ≥ 0 = x-2 jika x ≥ 2

• -(x-2) jika x-2 < 0 = -x+2 jika x < 2

* |2x+1| =

• 2x+1 jkka 2x+1 ≥ 0 = 2x+1 jika x ≥ -½

• -(2x+1) jika 2x+1 < 0 = -2x-1 jika x < -½

Gambar garis terlampir

1)Untuk x < -½

|x-2|+|2x+1| = 3

(-2x-1)+(-x+2) = 3

-3x+1 = 3

-3x = 2

x = -⅔ (✓)

2)Untuk -½≤ x <2

|x-2|+|2x+1| = 3

(-x+2)+(2x+1) = 3

x+3 = 3

x = 0 (✓)

3)Untuk x ≥ 2

|x-2|+|2x+1| = 3

(x-2)+(2x+1) = 3

3x-1 = 3

3x = 4

x = 4/3 (X)

HP = {0, -⅔}

(C)

7. Diketahui:

|3x+9| > 12

Ditanyakan:

HP

Jawab:

|3x+9| > 12

|3x+9|² > 12²

9x²+54x+81 > 144

x²+6x+9 > 16

x²+6x+9-16 > 0

x²+6x-7 > 0

Cari Batas

x²+6x-7 = 0

(x+7)(x-1) = 0

x = -7 atau x = 1

HP = {x| x<-7 atau x>1}

(B)

Mapel: Matematika

Kelas: 10

Materi: Persamaan dan Pertidaksamaan Nilai Mutlak

Answer 2

Jawab:

1. B

2. E

3. E

4. D

5. E

Penjelasan dengan langkah-langkah:

1.

14x +35 = 9x- 30

14x - 9x = - 30 - 35

5x = - 65

x = -65/5

x = -13

nilai x + 8/2-x = (-13+8)/(2-(-13) = -5/15 = - 1/3

2.

-5 < 4x + 3 < 7

-3-5 < 4x < 7 - 3

-8 < 4x < 4

-8/4 < x < 4/4

-2<x< 1

3.

I5x-15I = 10

(i) 5x - 15 = 10

5x = 10 + 15

5x = 25

x = 5

(ii) 5x-15 = -10

5x = -10 + 15

5x = 5

x = 5/5

x = 1

4.

I3x-7I = I2x+5I

(3x-7)²=(2x+5)²

(i) (3x-7) = (2x+5)

3x -2x = 7 + 5

x = 12

(ii) 3x-7 = -(2x+5)

3x+2x = - 5 + 7

5x = 2

x = 2/5

5.

f(2) = I3.2-9I =I6-9I = I-3I = 3