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Lea3viz

a)

[tex]2x - 3 = 8[/tex]

[tex]2x = 8 + 3[/tex]

[tex]2x = 11[/tex]

[tex]x = \frac{11}{2} = 5 \frac{1}{2} [/tex]

b)

[tex]4x = 5x - 2[/tex]

[tex]4x - 5x = - 2[/tex]

[tex] - x = - 2[/tex]

[tex]x = 2[/tex]

c)

[tex]5x - 12 = 4 + 4x[/tex]

[tex]5x - 4x = 4 + 12[/tex]

[tex]x = 16[/tex]

d)

[tex]9x - 8 = 3x + 2[/tex]

[tex]9x - 3x = 2 + 8[/tex]

[tex]6x = 10[/tex]

[tex]x = \frac{10}{6} = \frac{5}{3} = 1 \frac{2}{3} [/tex]

e)

[tex]10x - 4 = 5x + 8[/tex]

[tex]10x - 5x = 8 + 4[/tex]

[tex]5x = 12[/tex]

[tex]x = \frac{12}{5} = 2 \frac{2}{5} [/tex]

f)

[tex]2x - 2 = 12x + 18[/tex]

[tex]2x - 12x = 18 + 2[/tex]

[tex] - 10x = 20[/tex]

[tex]x = - 2[/tex]

g)

[tex]4 - 5(x + 2) = 3 - 5x[/tex]

[tex]4 - 5x - 10 = 3 - 5x[/tex]

[tex] - 5x + 5x = 3 - 4 + 10[/tex]

[tex]0 = 9[/tex]

równanie sprzeczne, 0 ≠ 9

h)

[tex]6x - 3 = 2x + 5[/tex]

[tex]6x - 2x = 5 + 3[/tex]

[tex]4x = 8[/tex]

[tex]x = 2[/tex]

i)

[tex]2x + 6 = 12[/tex]

[tex]2x = 12 - 6[/tex]

[tex]2x = 6[/tex]

[tex]x = \frac{6}{2} = 3[/tex]

j)

[tex]3x - 4 = 17[/tex]

[tex]3x = 17 + 4[/tex]

[tex]3x = 21[/tex]

[tex]x = \frac{21}{3} = 7[/tex]

k)

[tex]4 - 2x = 10[/tex]

[tex] - 2x = 10 - 4[/tex]

[tex] - 2x = 6[/tex]

[tex]x = \frac{6}{ - 2} = - 3[/tex]

l)

[tex]x + 6 = 2x + 3[/tex]

[tex]x - 2x = 3 - 6[/tex]

[tex] - x = - 3[/tex]

[tex]x = 3[/tex]

m)

[tex]2x + 4 = 4 - 3x[/tex]

[tex]2x + 3x = 4 - 4[/tex]

[tex]5 x = 0[/tex]

[tex]x = \frac{0}{5} = 0[/tex]

n)

[tex]3x + 11 = 6x - 1[/tex]

[tex]3x - 6x = - 1 - 11[/tex]

[tex] - 3x = - 12[/tex]

[tex]x = \frac{ - 12}{ - 3} = 4[/tex]

o)

[tex]2(x + 1) = 5[/tex]

[tex]2x + 2 = 5[/tex]

[tex]2x = 5 - 2[/tex]

[tex]2x = 3[/tex]

[tex]x = \frac{3}{2} = 1 \frac{1}{2} [/tex]

p)

[tex]2(x + 4) = 8 + 2x[/tex]

[tex]2x + 8 = 8 + 2x[/tex]

[tex]2x - 2x = 8 - 8[/tex]

[tex]0 = 0[/tex]

jest to równanie tożsamościowe

q)

[tex]2x - (3x + 1) = 6[/tex]

[tex]2x - 3x - 1 = 6[/tex]

[tex]2 x - 3x = 6 + 1[/tex]

[tex] - x = 7[/tex]

[tex]x = \frac{7}{ - 1} = - 7[/tex]

r)

[tex]2(x + 1) + x = 3x[/tex]

[tex]2x + 2 + x = 3x[/tex]

[tex]2x + x - 3x = - 2[/tex]

[tex]0 = - 2[/tex]

równanie sprzeczne, 0 ≠ -2

s)

[tex]2 - (5 + x) = 2(3 - x)[/tex]

[tex]2 - 5 - 5 = 6 - 2x[/tex]

[tex]2x = 6 - 2 + 5 + 5[/tex]

[tex]2x = 14[/tex]

[tex]x = \frac{14}{2} = 7[/tex]

Magdalena2038viz

a) 2x = 8 + 3

2x = 11 / ;2

X = 5,5

b) 4x = 5x - 2

4x - 5x = -2

-1x = -2 / : (-1)

X= 2

c) 5x -12 = 4 + 4x

5x - 4 = 4 + 12

1x = 16 / : (-1)

X= 16

d) 9x - 8 = 3x +2

9x - 3x = 2 + 8

6x = 10 /:(-6)

X = -1,66

e) 10x - 4 = 5x +8

10x - 5x = 8 + 4

5x = 12 /:(-5)

x = -2,4

f) 2x - 2 = 12x + 18

2x - 12x = 18 + 2

-10x = 20 /:(-10)

x = 2

g) 4 - 5(x+2) = 3 - 5x

4 - 5x + 10 = 3 - 5x

-5 + 5x = 3 -4 - 10

x = 0

h) 6x - 3 = 2x + 5

6x - 2x = 5 + 3

4x = 8 /:(-4)

x = -2

i) 2x + 6 = 12

2x = 12 - 6

2x = 6 /:(-2)

x = -3

j) 3x - 4 = 17

3x = 17 + 4

3x = 21 /:(-3)

x = -7

k) 4 - 2x = 10

-2x = 10 - 4

-2x = 6 /:(-2)

x = -3

l) x + 6 = 2x + 3

x - 2x = 3 - 6

-1x = -3 /:(-1)

x = 3

m) 2x + 4 = 4 - 3x

2x + 3x = 4 - 4

5x = 0

x = 0

n) 3x + 11 = 6x - 1

3x - 6x = -1 - 11

-3x = -12 /:(-3)

x = 4

o) 2(x+1) = 5

2x + 2 = 5

2x = 5 - 2

2x = 3 /:(-2)

x = -1,5

p) 2(x+4) = 8 + 2x

2x + 8 = 8 + 2x

2x - 2x = 8 - 8

x(0) = 0

q) 2x - (3x + 1) = 6

2x - 3x + 1 = 6

2x - 3x = 6 - 1

-1x = 5 /:(-1)

x = -5

r) 2(x+1) + x = 3x

2x + 2 + x = 3x

2x + x - 3x = -2

x = -2

s) 2 - (5 + x) = 2(3-x)

2 - 5 + x = 6 - 2x

x + 2x = 6 -2 + 5

3x = 9 / :(-3)

x = -3

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