Question

Me ajude por favor nesse trabalho vale 3 pontos De o valor de x". A) 12-x/4 = 10/8 b) x-12/4 = x/8 c) x-14/x = 5/15 d) x-10/4 = 2/8 e) 4/7 = 12/16+x

Answer 1

Me ajude por favor nesse trabalho vale 3 pontos De o valor de x". A) 12-x/4 = 10/8 b) x-12/4 = x/8 c) x-14/x = 5/15 d) x-10/4 = 2/8 e) 4/7 = 12/16+x


A) 12-x/4 = 10/8 mmc(4,8) 4,8| 2
2,4| 2
x 10 1,2| 2
12 - ------- = -------- 1,1/ = 2.2.2 = 8
4 8

8(12) - 2(x) = 1(10)
------------------------------- fração com IGUALDADE desprezamos o denominador
8

8(12) - 2(x) = 1(10)

96 - 2x = 10
- 2x = 10 - 96
- 2x = - 86
x = - 86/-2
x = + 86/2
x = 43

b) x-12/4 = x/8

12 x
x - ------- = --------
4 8 mm(4,8) = 8 (idem acima) IIGUAL


8(X) - 2(12) = 1(X)
---------------------------idem instrução acima
8
8(x) - 2(12) =1(x)
8x - 24 = 1x
8x - 1x = + 24
7x = 24
x = 24/7


c) x-14/x = 5/15

14 5
x - -------- = ----- mmc(15, x ) = 15x
x 15

15x(x) - 15(14) = x(5)
--------------------------- idem acima
15x

15x(x) - 15(14) = x(5)
15x² - 210 = 5x -------------iguala a ZERO
15X² - 210 - 5X = 0 ----------------ARRUMAR A CASA
15x² - 5x - 210 = 0 equação do 2º grau achar as raizes

15x² - 5x - 210 = 0
a = 15
b = - 5
c = - 210
Δ = b² - 4ac
Δ = (-5)² - 4(15)(-210)
Δ = + 25 + 12.600
Δ = 12.625                                                 fatorar 12.625| 5
                                                                                2.525| 5
                                                                                    505| 5
                                                                                     101| 101
                                                                                       1
√12.625 = √5.5.5.101 = √5².5.101 = 5√5.101 = 5√505
Δ = 12.625 ==== √Δ = 5√505


(baskara)
x = - b - + √Δ/2a
x' = - (-5) - √12.625/2(15)
x' = + 5 - 5√505/30

         5 - 5√505   : 5          1 - √505
x' = ---------------------- = ----------------
             30          : 5                6


x" =  -(-5) + √12.625/2(15)
x" = + 5 + 5√505/30

         5 + 5√505 : 5          1 + √505
x" = ------------------    =  ---------------
                    30  : 5                6


d) x-10/4 = 2/8
        10          2
x -  ------- = ------
          4          8

8(x) - 2(10) = 1(2)      idem acima
------------------------------
                8

8(x) - 2(10) = 1(2)
8x -20  = 2
8x = 2 + 20
8x = 22
x = 22/8 ---------------------divide AMBOS por 2(simplificar)
x = 11/4


e) 4/7 = 12/16+x

4             12
----- =  -------- + x                 mmc(7,16) = 7x16 = 112
 7            16

16(4) = 7(12) + 112(x)       idem acima
--------------------------
                112

16(4) = 7(12) + 112(x)

64 = 84 + 112x
64 - 84 = 112x
- 20 = 112x

112x = - 20
x = - 20/112 -----------------divide AMBOS  por 4 (simplificar a fração)
x = - 5/28