Question

1. Rozwiąż równanie.Pomoże ktoś?
a) x-(2x-1)-2x = 2(3x-4)
b) 3(x−2)−(x−3)=-(5x−4)
c) -(5x-3) = 2(4-x) - 3x
d) -2(5x-7) - 3x = 2(x-8)
e) 2x+(-3x+4)=-4(3x-1)
f) (5-x)-(x+1)-9 = -(2x+5)
g) -(5x+4)+(x-1)-(1-x) = 0
h) 4x-8-(x+3)+2x = -(2x-3)

Answer 1

Verified answer

a)

[tex]x - (2x - 1) - 2x = 2(3x - 4) \\x - 2x + 1 - 2x = 6x - 8 \\ - 3x + 1 = 6x - 8\\ - 3x - 6x = - 8 - 1\\ - 9x = - 9 \\ 9x = 9 | \div 9\\ x = 1[/tex]

b)

[tex]3(x - 2) - (x - 3) = - (5x - 4) \\ 3x - 6 - x + 3 = - 5x + 4 \\ 3x - x + 5x = 6 - 3 + 4 \\ 7x = 7 | \div 7 \\ x = 1[/tex]

c)

[tex] - (5x - 3) = 2(4 - x) - 3x \\ - 5x + 3 = 8 - 2x - 3x \\ - 5x + 3 = 8 - 5x \\ 3 = 8 \\ \: rownanie \: sprzeczne[/tex]

d)

[tex] - 2(5x -7 ) - 3x = 2(x - 8) \\ - 10x + 14 - 3x = 2x - 16 \\ - 13x + 14 = 2x - 16 \\ - 13x - 2x = - 14 - 16 \\ - 15x = - 30 \\ 15x = 30 | \div 15 \\ x = 2[/tex]

e)

[tex]2x + ( - 3x + 4) = - 4(3x - 1) \\ 2x - 3x + 4 = - 12x + 4 \\ - x + 4 = - 12x + 4 \\ - x + 12x = - 4 + 4 \\ 11x = 0 \\ rownanie \: sprzeczne[/tex]

f)

[tex](5 - x) - (x + 1) - 9 = - (2x + 5) \\ 5 - x - x - 1 - 9= - 2x - 5 \\ 5 - 2x - 1 - 9 = - 2x - 5 \\ - 5 - 2x = - 2x - 5 \\ 0 = 0 \\ rownanie \: tozsamosciowe[/tex]

g)

[tex] - (5x + 4) + (x - 1) - (1 - x) = 0 \\ - 5x - 4 + x - 1 - 1 + x = 0 \\ - 3x - 6 = 0 \\ - 3x = 0 + 6 \\ - 3x = 6 \\ 3x = - 6 | \div 3\\ x = - 2[/tex]

h)

[tex]4x - 8 - (x + 3) + 2x = - (2x - 3) \\ 4x - 8 - x - 3 + 2x = - 2x + 3 \\ 5x - 8 - 3 = - 2x + 3 \\ 5x - 11 = - 2x + 3 \\ 5x + 2x = 11 + 3 \\ 7x = 14 | \div 7 \\ x = 2[/tex]