Question

Решите уравнение: |x+6|-|4x-5|=15

Answer 1

|x + 6| - |4x - 5| = 15

x < - 6
-x - 6 + 4x - 5 = 15
3x - 11 = 15
3x = 26
$left { {{x textless -6} atop {x=frac{26}{3} }} right.$
x ∈ ∅

-6 ≤ x < 5/4
x + 6 + 4x - 5 = 15
5x + 1 = 15
5x = 14
$left { {{-6 leq x textless frac{5}{4} } atop {x= frac{14}{5} }} right.$
x ∈ ∅

x ≥ 5/4
x + 6 - 4x + 5 = 15
11 - 3x = 15
3x = -4
$left { {{x geq frac{5}{4} } atop {x=- frac{4}{3} }} right.$
x ∈ ∅

Уравнение не имеет решений: x ∈ ∅.