Question

8. Determine a raiz das seguintes equações do 1º grau com uma incógnita:

a)
$\frac{ x}{2} + 1 = \frac{x}{5} + \frac{1}{4}$
b)
$\frac{x}{4} + \frac{x}{3} = x - 100$
c)
$\frac{2x}{3} + \frac{5x}{6} = \frac{1}{2}$
​

Answer 1

Resposta:

a ) x = - 2.5

b ) x = 120

c ) x = 1 / 3

Explicação passo-a-passo:

a )

( x / 2 ) + 1 = ( x / 5 ) + ( 1 / 4 )

( x / 2 ) + ( 2 / 2 ) = ( 4x / 20 ) + ( 5 / 20 )

( x + 2 ) / 2 = ( 4x + 5 ) / 20

20 ( x + 2 ) = 2 ( 4x + 5 )

20 ( x + 2 ) / 2 = 4x + 5

10 ( x + 2 ) = 4x + 5

10x + 20 = 4x + 5

10x - 4x = 5 - 20

6x = - 15

x = - 15 / 6

= - 5 / 2

x = - 2.5

b )

( x / 4 ) + ( x / 3 ) = x - 100

( 3x / 12 ) + ( 4x / 12 ) = x - 100

( 3x + 4x ) / 12 = x - 100

7x / 12 = x - 100

7x = 12 ( x - 100 )

7x = 12x - 1200

7x - 12x = - 1200

- 5x = - 1200

5x = 1200

x = 1200 / 5

x = 240

c )

( 2x / 3 ) + ( 5x / 6 ) = 1 / 2

( 4x + 6 ) + ( 5x / 6 ) = 1 / 2

( 4x + 5x ) / 6 = 1 / 2

9x / 6 = 1 / 2

9x = 6 / 2

9x = 3

x = 3 / 9

x = 1 / 3