Question

1. Considerando U = R determine a solução das seguintes equações de 1 de grau com uma incógnita:
a) 21x - 17 = 109
b) 73x + 100 = 53x
c) 1.7 + 2.5x = 4.2
d) 23x - 22 = 19x + 6
e) 12x - 16 = - 21 + 10x
f) 1.9x - 3.6 = x - 10.8
g) 10(x + 1) - 5(x - 2) = 70
h) 5(x + 2) - 13 = 2(3x - 1)
i) 7(2 + x) = 5(x - 1, 2) + 35
j) 3(x + 1) - 2(x - 1) = - (x + 5) ​

Answer 1

Resposta:

$a) \: 21x - 17 = 109 \\ 21x = 109 + 17 \\ 21x = 126 \\ \\ x = \frac{126}{21} \\ \\ x = 6$

$b) \: 73x + 100 = 53x \\ 73x + 100 - 53x = 0 \\ 20x = - 100 \\ \\ x = - \frac{100}{20} \\ \\ x = - 5$

$c) \: 1.7 + 2.5x = 4.2 \\ 2.5x = 4.2 - 1.7 \\ 2.5x = 2.5 \\ \\ x = \frac{2.5}{2.5} \\ \\ x = 1$

$d) \: 23x - 22 = 19x + 6 \\ 23x - 22 - 19x - 6 = 0 \\ 4x - 28 = 0 \\ 4x = 28 \\ \\ x = \frac{28}{4} \\ \\ x = 7$

$e) \: 12x - 16 = - 21 + 10x \\ 12x - 16 + 21 - 10x = 0 \\ 2x + 5 = 0 \\ 2x = - 5 \\ \\ x = - \frac{5}{2}$

$f) \: 1.9x - 3.6 = x - 10.8 \\ 1.9x - 3.6 - x + 10.8 = 0 \\ 0.9x + 7.2 = 0 \\ 0.9x = - 7.2 \\ \\ x = - \frac{7.2}{0.9} \\ \\ x = - 8$

$g) \: 10 \times (x + 1) - 5 \times (x - 2) = 70 \\ 10x + 10 - 5x + 10 = 70 \\ 5x = 70 - 20 \\ 5x = 50 \\ \\ x = \frac{50}{5} \\ \\ x = 10$

$h) \: 5 \times (x + 2) - 13 = 2 \times (3x - 1) \\ 5x + 10 - 13 = 6x - 2 \\ 5x - 3 - 6x + 2 = 0 \\ - x - 1 = 0 \\ - x = 1 \times ( - 1) \\ x = - 1$

$i) \: 7 \times (2 + x) = 5 \times (x - 1.2) + 35 \\ 14 + 7x = 5x - 6 + 35 \\ 14 + 7x = 5x + 29 \\ 14 + 7x - 5x - 29 = 0 \\ 2x - 15 = 0 \\ 2x = 15 \\ \\ x = \frac{15}{2}$

$j) \: 3 \times (x + 1) - 2 \times (x - 1) = - (x + 5) \\ 3x + 3 - 2x + 2 = - x - 5 \\ x + 5 + x + 5 = 0 \\ 2x + 10 = 0 \\ 2x = - 10 \\ \\ x = - \frac{10}{2} \\ \\ x = - 5$