Jawaban :

A. HP = { 3, -2 }

B. HP = { -8, -4}

C. x = 1/2

Penjelasan dengan langkah-langkah :

A. |2x-1| = 5

|2x-1| = 5

√(2x-1)² = 5 (kuadrat kan keduanya)

(2x-1)² = 25

(2x-1) (2x-1) = 25

4x² - 4x + 1 = 25

4x² - 4x - 24 = 0 (bagikan dengan 4)

x² - x - 6 = 0

(x-3) (x+2) = 0

x - 3 = 0 ✓ x + 2 = 0

x = 3 x = -2

Jadi, HP = { 3, -2 }

B. |x+2|=6

|x+2|=6

√(x+2)² = 6 (kuadrat kan keduanya)

(x+2)² = 36

(x+2) (x+2) = 36

x² + 4x + 4 = 36

x² + 4x + 32 = 0

(x+8) (x+4) = 0

x + 8 = 0 ✓ x + 4 = 0

x = -8 x = -4

Jadi, HP = { -8, -4}

C. |x+1| = |x-2|

cara pertama

|x - 2| = |x + 1|

x - x = -2 - 1

0 = -3 (tidak valid)

x + 1 = -x + 2

x + x = 2 - 1

2x = 1

x = 1/2

Jadi, x = 1/2

cara kedua

|x - 2| = |x + 1|

|x - 2|² = |x + 1|²

(x - 2)² = (x + 1)²

(x - 2)² - (x + 1)² = 0

a b

a² - b² = (a+b) (a-b)

sehingga

((x - 2) + (x + 1)) ((x - 2) - (x + 1)) = 0

(x - 2 + x + 1) (x - 2 - x - 1) = 0

(2x - 1) (-3) = 0

2x - 1 = 0 ✓ -3 =0

2x - 1 = 0

x = ½

-3 = 0 (tidak valid)

Jadi, x = 1/2