Question

Tentukan nilai X dari persamaan nilai mutlak berikut:
a) | 3x + 2 | = 5
b) | 3 - x | = 5
c) | x - 2 | = | 2x - 1 |
d) | x - 2 | = | 3 - 2x |

Mohon bantuan nya...

Answer 1

a) | 3x + 2 | = 5
3x + 2 = 5
3x = 3
x = 1

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

b) | 3 - x | = 5
3 - x = 5
-x = 2
x = -2

-(3 - x) = 5
-3 + x = 5
x = 8

c) | x - 2 | = | 2x - 1 |
kedua ruas dikuadratkan, maka
(x - 2)² = (2x - 1)²
x² - 4x + 4 = 4x² - 4x + 1
3x² - 3 = 0
3x² = 3
x² = 1
x = 1

d) | x - 2 | = | 3 - 2x |
kedua ruas dikuadratkan, maka
(x - 2)² = (3 - 2x)²
x² - 4x + 4 = 9 - 12x + 4x²
3x² - 8x - 5 = 0
(3x - 5)(x + 1) = 0

3x - 5 = 0
3x = 5
x = 5/3

x + 1 = 0
x = -1