x-3-2-1-solve-for-real-x-

Question Number 81519 by ajfour last updated on 13/Feb/20

∣∣∣ x ∣ - 3 ∣ - 2 ∣= 1

s o l v e f o r r e a l x .

Commented by mr W last updated on 13/Feb/20

∣∣∣ x ∣ - 3 ∣ - 2 ∣= 1

∣∣ x ∣ - 3 ∣ - 2 = \pm 1

∣∣ x ∣ - 3 ∣= 2 \pm 1

∣ x ∣ - 3 = \pm (2 \pm 1)

∣ x ∣= 3 \pm (2 \pm 1)

\Rightarrow x = \pm [3 \pm (2 \pm 1)] = 0, \pm 2, \pm 4, \pm 6

Commented by ajfour last updated on 13/Feb/20

y e s s i r, a l l c o r r e c t; w h a t i f

∣∣∣ x ∣ - 3 ∣ - 2 ∣=∣ x ∣ / 4 ?

Commented by mr W last updated on 13/Feb/20

t =∣ x ∣

∣∣ t - 3 ∣ - 2 ∣= \frac{t}{4}

∣ t - 3 ∣= 2 \pm \frac{t}{4}

t = 3 \pm (2 \pm \frac{t}{4})

t = 3 + (2 + \frac{t}{4}) \Rightarrow t = \frac{20}{3} \Rightarrow x = \pm \frac{20}{3}

t = 3 + (2 - \frac{t}{4}) \Rightarrow t = 4 \Rightarrow x = \pm 4

t = 3 - (2 + \frac{t}{4}) \Rightarrow t = \frac{4}{3} \Rightarrow x = \pm \frac{4}{3}

t = 3 - (2 - \frac{t}{4}) \Rightarrow t = \frac{4}{5} \Rightarrow x = \pm \frac{4}{5}

Commented by ajfour last updated on 13/Feb/20

W o n d e r f u l, S i r, v e r y b e a u t i f u l!

Answered by behi83417@gmail.com last updated on 13/Feb/20

x = \pm 2, \pm 4