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Răspuns:

Explicație pas cu pas:

a) 3-2x = -7 => 2x = 3+7 => 2x = 10 => x = 10:2 => x = 5 ∈ R

11(x-4) = 3²+2 => 11x-44 = 9+2 => 11x = 44+11 => x = 55:11 => x = 5 ∈ R

Ecuatiile sunt echivalente

b) 6+5x = 2(-3+x) => 6+5x = -6+2x => 5x-2x = -6-6 => 3x = -12 =>

x = -12:3 => x = -4 ∈ Z

x+18 = 2(-1-x)+8 => x+18 = -2-2x+8 => x+2x = -18+6 =>

3x = -12 => x = -12:3 => x = -4 ∈ Z =>

Ecuatiile sunt echivalente

c) 7x-5(x-1) = 10x-3 => 7x-5x+5 = 10x-3 =>

10x-2x = 5+3 => 8x = 8 => x = 1 ∈ R

4x-3(2-x) = 4 => 4x-6+3x = 4 => 7x = 10 => x = 10/7 ∈ R =>

Ecuatiile nu sunt echivalente

d) 13x+41 = 5(2x+7)+3 => 13x+41 = 10x+35+3 =>

13x-10x = 38-41 => 3x = -3 => x = -1 ∈ R

9(x-2)+14 = -2(3-4x)+1 => 9x-18+14 = -6+8x+1 =>

9x-8x = 4-5 => x = -1 ∈ R =>

Ecuatiile sunt echivalente

Răspuns:

Explicație pas cu pas:

Ecuatiile sunt echivalente daca au aceleasi solutii.

a) 3-2x=-7  ⇔ 3+7=2x  ⇔ 10=2x  ⇔ x=5

   11(x-4)=3²+2  ⇔ 11x-44=9+2  ⇔ 11x=44+11  ⇔ 11x=55  ⇔ x=5

Cele doua ecuatii sunt echivalente, ambele au solutia x=5.

b) 6+5x=2(-3+x)  ⇔ 6+5x=-6+2x  ⇔ 5x-2x=-6-6  ⇔ 3x=-12  ⇔ x=-4

x+18=2(-1-x)+8  ⇔ x+18=-2-2x+8  ⇔ x+2x=-18-2+8  ⇔ 3x=-12  ⇔ x=-4

Cele doua ecuatii sunt echivalente, ambele au solutia x=-4

c) 7x-5(x-1)=10x-3  ⇔ 7x-5x+5=10x-3  ⇔ 2x+5=10x-3  ⇔ 8=8x  ⇔ x=1

  4x-3(2-x)=4  ⇔ 4x-6+3x=4  ⇔ 7x-6=4  ⇔ 7x=10  ⇔ x=10/7

Cele doua ecuatii nu sunt echivalente deoarece nu au solutii egale, prima are solutia x=-1 iar a doua are solutia x=10/7

d) 13x+41=5(2x+7)+3 ⇔ 13x+41=10x+35+3 ⇔ 13x-10x=38-41 ⇔ 3x=-3  ⇔ x=-1

9(x-2)+14=-2(3-4x)+1  ⇔ 9x-18+14=-6+8x+1  ⇔ 9x-4=8x-5  ⇔ 9x-8x=-5+4  ⇔ x=-1  

Cele doua ecuatii sunt echivalente, ambele au solutia x=-1