Question

1) Resolva as equações, sendo U= Q;
a) 4x – 7 = 8x – 2

b) 9x + 9 + 3x = 15

c) 16x – 1 = 12x + 3

d) 3x -2 = 4x + 9

e) x + x – 4 = 17 – 2x + 1

2) Resolva as seguintes equações, sendo U = Q:
a) 3.( 2x – 1) = - 2 .( x + 3 )

b) 5x – 3. ( x + 2 ) = 15

c) 3.( x – 2 ) = 4. ( 3 – x )

d) 7.( x – 4) = 2 x – 3

e) 5. ( x – 3 ) – 4 .( x + 2 ) = 2 + 3.( 1- 2x)

Answer 1

Resposta:

1) Resolva as equações, sendo U= Q;

a) 4x – 7 = 8x – 2

$4x - 7 - 8x + 2 = 0 \\ - 4x - 5 = 0 \\ - 4x = 5 \times ( - 1) \\ 4x = - 5 \\ \\ x = - \frac{5}{4}$

b) 9x + 9 + 3x = 15

$9x + 9 + 3x - 15 = 0 \\ 12x - 6 = 0 \\ 12x = 6 \\ \\ x = \frac{6}{12} \div (6) \\ \\ x = \frac{1}{2}$

c) 16x – 1 = 12x + 3

$16x - 1 - 12x - 3 = 0 \\ 4x - 4 = 0 \\ 4x = 4 \div (4) \\ x = 1$

d) 3x -2 = 4x + 9

$3x - 2 - 4x - 9 = 0 \\ - x - 11 = 0 \\ - x = 11 \times ( - 1) \\ x = - 11$

e) x + x – 4 = 17 – 2x + 1

$2x - 4 = 18 - 2x \\ 2x - 4 - 18 + 2x = 0 \\ 4x - 22 = 0 \\ 4x = 22 \\ \\ x = \frac{22}{4} \div (2) \\ \\ x = \frac{11}{2}$

2) Resolva as seguintes equações, sendo U = Q:

a) 3.( 2x – 1) = - 2 .( x + 3 )

$6x - 3 = - 2x - 6 \\ 6x - 3 + 2x + 6 = 0 \\ 8x + 3 = 0 \\ 8x = - 3 \\ \\ x = - \frac{3}{8}$

b) 5x – 3. ( x + 2 ) = 15

$5x - 3x - 6 = 15 \\ 2x - 6 = 15 \\ 2x - 6 - 15 = 0 \\ 2x - 21 = 0 \\ 2x = 21 \\ \\ x = \frac{21}{2}$

c) 3.( x – 2 ) = 4. ( 3 – x )

$3x - 6 = 12 - 4x \\ 3x - 6 - 12 + 4x = 0 \\ 7x - 18 = 0 \\ 7x = 18 \\ \\ x = \frac{18}{7}$

d) 7.( x – 4) = 2 x – 3

$7x - 28 = 2x - 3 \\ 7x - 28 - 2x + 3 = 0 \\ 5x - 25 = 0 \\ 5x = 25 \div (5) \\ x = 5$

e) 5. ( x – 3 ) – 4 .( x + 2 ) = 2 + 3.( 1- 2x)

$5x - 15 - 4x - 8 = 2 + 3 - 6x \\ x - 23 = 5 - 6x \\ x - 23 - 5 + 6x = 0 \\ 7x - 28 = 0 \\ 7x = 28 \div (7) \\ x = 4$