Question

Resolva as equações
abaixo:
a) 16 + 8y = 3y + 81


b) 5x = 12x + 49


c) 6 ( – 3x + 5 ) – 4 ( 2x + 2 ) = –3 ( 6
+ 8x )


d) 2x ( 4x – 1 ) = 21

Answer 1

a) 16 + 8y = 3y + 81
8y - 3y = 81 -16
5y= 65
y= $\frac{65}{5}$
y= 13

b) 5x = 12x + 49
5x - 12x = 49
-7x = 49 . (-1)
7x=49
x= $\frac{49}{7}$
x=7

c) 6 ( – 3x + 5 ) – 4 ( 2x + 2 ) = –3 ( 6+ 8x )
-18x + 30 - 8x - 8 = - 18 - 24x
-18x -8x +24x= -18 -30 +8
-26x + 24x= - 48 +8
-2x= - 40 . (-1)
2x= 40
x= $\frac{40}{2}$
x=20

d) 2x ( 4x – 1 ) = 21
8x² - 2x =21
8x² - 2x -21
Δ= b²-4 ac
Δ= (-2)² - 4.8.(-21)
Δ=4 +672
Δ= 676

x= -b +/- √Δ/2a
x= - (-2) +/- √676 / 2.8
x' =2 + 26 / 16
x'= 28/16
x''= 2-26/ 16
x''= -24/16

Answer 2

a) 8y - 3y = 81 - 16
5y = 65
y = 65/ 5
y =13

b) 5x - 12x = 49
-7x = 49 (-1)
7x = -49
x = -49/7
x = - 7

c) -18x + 30 - 8x - 8 = -18 - 24x
- 18x - 8x + 24x = -18 + 8 -30
- 2x = - 40 (-1)
2x = 40
x = 40/2
x = 20

d) 8x² - 2x = 21
8x² - 2x - 21 = 0
a = 8
b = -2
c = -21
Δ = b² - 4ac
Δ = (-2)² - 4.8.(-21)
Δ = 4 + 672
Δ = 676
x = -b +- √Δ/2a
x = -(-2) +- √676/2.8
x = 2 +- 26/16
x' = 2+26/16 ⇒x' = 28/16 ⇒x' = 7/4
x" = 2 - 26/ 16 ⇒ x" = - 24/16 ⇒ x" = - 3/2

S = { 7/4 ; - 3/2}