Bab 1 Fungsi, Persamaan, dan Pertidaksamaan Eksponensial
LKS 8
Soal dan Jawaban Matematika Kelas X Sukino
Kunci Jawaban Matematika Sukino
16. Nilai x yang memenuhi pertidaksamaan
3β(2xβ (4x - 13 3β16x + 2 ))β€ 1/β16x 3β4
adalah...
a. x β€ 16/13
b. x β€ 13/16
c. x β€ 0
d. x β₯ -13/16
e. x β€ - 16/13
Jawaban : A
3β(2xβ (4x - 13 3β16x + 2 ))
= 3β(2xβ (4x - 13 3β24x + 8 ))
= 3β(2xβ (22x - 26 2(4x + 8)/3 ))
= 3β(2xβ (22x - 26 + (4x + 8)/3 ))
= 3β(2xβ (2(6x - 78 + 4x + 8)/3 ))
= 3β(2x 2(6x - 78 + 4x + 8)/6 )
= 3β(2(6x - 78 + 4x + 8 + 6x)/6 )
= 2(6x - 78 + 4x + 8 + 6x)/18
1/β16x 3β4
=1/β16x 22/3
=1/β24x 22/3
=1/β24x + 2/3
=1/β2(12x + 2)/3
=1/2(12x + 2)/6
=2(-12x - 2)/6
2(6x - 78 + 4x + 8 + 6x)/18 β€ 2(-12x - 2)/6
(6x - 78 + 4x + 8 + 6x)/18 β€ (-12x - 2)/6
(16x - 70)/18 β€ (-12x - 2)/6
(16x - 70)/18 β€ (-36x - 6)/18
16x + 36x - 70 + 6 β€ 0
52x - 64 β€ 0
x β€ 64/52
x β€ 16/13
>> soal no 17
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