Question

1º) Resolva as seguinte equações:
a) 4x – 7 = 8x – 2

b) 2y + 1 = 4y – 7

c) 16m – 1 = 12m + 3

d) 5x – 3 + x = 2x + 9

e) 5y + 6y – 16 = 3y + 2y – 4

f) 5a + 4 = 3a – 2a + 4

g) a + 2a + 3 – 5a = 4a – 9

h) 4x – 1 = 3.( x – 1 )

i) 2.( y – 1 ) = 3y + 4

j) 5x – 3.( x + 2 ) = 15

k) 2x + 3x + 9 = 8.( 6 – x )

l) 3.( 2y + 3 ) – 4.( y – 1 ) = 3

Answer 1

Explicação passo-a-passo juntamente com as respostas:

$a) \\ 4x - 7 = 8x - 2 \\ 4x - 8x = - 2 + 7 \\ ( - 1) - 4x = 5 ( - 1)\\ 4x = - 5 \\ x = \frac{ - 5}{4}$

$b) \\ 2y + 1 = 4y - 7 \\ 2y - 4y = - 7 - 1 \\ ( - 1) \: \: - 2y = - 8 \: \: ( - 1) \\ 2y = 8 \\ y = \frac{8}{2} \\ y = 4$

$c) \\ 16m - 1 = 12m + 3 \\ 16m - 12m = 3 + 1 \\ 4m = 4 \\ m = \frac{4}{4} \\ m = 1$

$d) \\ 5x - 3 + x = 2x + 9 \\ 5x + x - 2x = 9 + 3 \\ 4x = 12 \\ x = \frac{12}{4} \\ x = 3$

$e) \\ 5y + 6y - 16 = 3y + 2y - 4 \\ 5y + 6y - 3y - 2y = - 4 + 16 \\ 11y - 5y = 12 \\ 6y = 12 \\ y = \frac{12}{6} \\ y = 2$

$f) = 5a + 4 = 3a - 2a + 4 \\ 5a - 3a + 2a = 4 - 4 \\ 7a - 3a = 0 \\ 4a = 0 \\ a = \frac{0}{4} \\ a = 0$

$g) \\ a + 2a + 3 - 5a = 4a - 9 \\ a + 2a - 5a - 4a = - 9 - 3 \\ 3a - 9a = - 12 \\ ( - 1) \: \: - 6a = - 12 \: \: \:( - 1) \\ 6a = 12 \\ a = \frac{12}{6} \\ a = 2$

$h) \\ 4x - 1 = 3.(x - 1) \\ 4x - 1 = 3x - 3 \\ 4x - 3x = - 3 + 1 \\ 1x = - 2 \\ x = \frac{ - 2}{1} \\ x = - 2$

$i) \\ 2.(y - 1) = 3y + 4 \\ 2y - 2 = 3y + 4 \\ 2y - 3y = 4 + 2 \\ ( - 1) - 1y = 6 ( - 1) \\ 1y = - 6 \\ y = \frac{ - 6}{1} \\ y = - 6$

$j) \\ 5x - 3.(x + 2) = 15 \\ 5x - 3x - 6 = 15 \\ 5x - 3x = 15 + 6 \\ 2x = 21 \\ x = \frac{21}{2}$

$k) \\ 2x + 3x + 9 = 8.(6 - x) \\ 2x + 3x + 9 = 48 - 8x \\ 2x + 3x + 8x = 48 - 9 \\ 13x = 39 \\ x = \frac{39}{13} \\ x = 3$

$l) \\ 3.(2y + 3) - 4.(y - 1) = 3 \\ 6y + 9 - 4y + 4 = 3 \\ 6y - 4y = 3 - 9 - 4 \\ 2y = 3 - 13 \\ 2y = - 10 \\ y = \frac{ - 10}{2} \\ y = - 5$