Răspuns:
Explicație pas cu pas:
a)
( x+3)/2 + x/4 + ( 2x+5)/6 = (x+1)/4 - 5/12 l × 12
6(x+3) + 3 x + 2(2x+5) = 3(x+1) - 5
6 x + 18 + 3 x + 4 x + 10 = 3 x + 3 - 5
13 x + 28 = 3 x - 2
13 x - 3 x = - 2 - 28
10 x = - 30
x = ( - 30 ) : 10
x = - 3 ∈ R
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b)
(2x-1)/20 + (x+2)/15 - 1/4 = (x+1)/12 + 7/12 l × 60
→ c.m.m.m.c al numitorilor 20; 15; 4 si 12 este 60
3(2x-1) + 4(x+2) - 15 = 5(x+1+7)
6 x - 3 + 4 x + 8 - 15 = 5 x + 40
10 x - 10 = 5 x + 40
10 x - 5 x = 40 + 10
5 x = 50
x = 50 : 5
x = 10
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c) 2 intregi si 11/12 = ( 2 ×12 + 11 ) /12 = 35/12
(2x+1)/3 + x/6 - 3/4 = 35/12 + (x-4)/2 l × 12
→ c.m.m.m.c al numitorilor 3; 6; 4; 12 si 2 este 12
4(2x+1) + 2 x - 9 = 35 + 6(x-4)
8 x + 4 + 2 x - 9 = 35 + 6 x - 24
10 x - 5 = 6 x + 11
10 x - 6 x = 11 + 5
4 x = 16
x = 16 : 4
x = 4
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d)
(8x-7)/7 - (2x+9)/6 = (6x+11)/14 - 5/21 l × 42
→ c.m.m.m.c al numitorilor 7; 6; 14 si 21 = 42
6(8x-7) - 7(2x+9) = 3(6x+11) - 10
48 x - 42 - 14 x - 63 = 18 x + 33 - 10
34 x - 105 = 18 x + 23
34 x - 18 x = 23 + 105
16 x = 128
x = 128 : 16
x = 8 ∈ R
