Question

Resolver las siguientes ecuaciones:
a) 4(2x-5)=1+x
b) x+1=3(x-5)
c) x+6=2x-3
d) 9-7x=31-5x
e) x+(x+1)=29

Answer 1

Explicación paso a paso:

$a) \\ 4(2x - 5) = 1 + x \\ 8x - 20 = 1 + x \\ 8x - x = 1 + 20 \\ 7x = 21 \\ x = 21 \div 7 \\ x = 3 \\ \\ comprobamos \\ 4(2 \times 3 - 5) = 1 + 3 \\ 4(6 - 5) = 4 \\ 4 \times 1 = 4 \\ 4 = 4$

$b) \\ x + 1 = 3(x - 5) \\ x + 1 = 3x - 15 \\ x - 3x = - 15 - 1 \\ - 2x = - 16 \\ x = - 16 \div ( - 2) \\ x = 8 \\ \\ comprobamos \\ 8 + 1 = 3(8 - 5) \\ 9 = 3(3) \\ 9 = 9$

$c) \\ x + 6 = 2x - 3 \\ x - 2x = - 3 - 6 \\ - 1x = - 9 \\ x = - 9 \div ( - 1) \\ x = 9\\ \\ comprobamos \\ 9 + 6 = 2 \times 9 - 3 \\ 15 = 18 - 3 \\ 15 = 15$

$d) \\ 9 - 7x = 31 - 5x \\ - 7x + 5x = 31 - 9 \\ - 2x = 22 \\ x = 22 \div ( - 2) \\ x = - 11 \\ \\ comprobamos \\ 9 - 7 \times ( - 11) = 31 - 5 \times ( - 11) \\ 9 + 77 = 31 + 55 \\ 86 = 86$

$e) \\ x + (x + 1) = 29 \\ x + x + 1 = 29 \\ 2x = 29 - 1 \\ 2x = 28 \\ x = 28 \div 2 \\ x = 14 \\ \\ comprobamos \\ 14 + (14 + 1) = 29 \\ 14 + 15 = 29 \\ 29 = 29$