Odpowiedź:
1) 8 - 2x = 3(5 - x)
8 - 2x = 15 - 3x
-2x + 3x = 15 - 8
x = 7 (B)
2) x² + 2x - 15 = 0
Δ = b² - 4ac = 2² - 4(1)(-15) = 4 + 60 = 64
[tex]\sqrt{delta}[/tex] = 8
x1 = (-b - [tex]\sqrt{delta}[/tex])/2a = (-2 - 8)/2 = -10/2 = -5 (A)
x2 = (-b + [tex]\sqrt{delta}[/tex])/2a = (-2 + 8)/2 = 6/2 = 3 (C)
3) Pierwszy kąt = 4x
Drugi kąt = x
Trzeci kąt = 4x - 27°
Ich suma: 180°
4x + x + 4x - 27° = 180
9x = 153°
x = 17°
Pierwszy kąt = 4 × 17 = 68°
Drugi kąt = 17°
Trzeci kąt = 68 - 27 = 41°
4) 3(x - 1) - 4(x - 2) = 2(x - 3)
3x - 3 - 4x + 8 = 2x - 6
-3x = -11
x = [tex]\frac{11}{3}[/tex] = 3[tex]\frac{2}{3}[/tex]
5) 1 - [tex]\frac{x+1}{3}[/tex] = [tex]\frac{x}{2}[/tex] I×6
6 - 2(x + 1) = 3x
6 - 2x - 2 = 3x
-5x = -4
x = [tex]\frac{4}{5}[/tex] = 0,75
