Question

Ayuda con mi tarea por favor.

Resuelve las siguientes ecuaciones y compruben que las soluciones sean correctas.


a) 3(x-1)=9

b) 2(3x+2)=40

c) 4(3+2x)=36

d) m-(7+m)=3m+(m-3)

e) 2b+3(3b+1)=25

f) 3+2(2x-3)=17

g) 3c-(4+2c)=0

h) x-4(5-x)=0

Answer 1

- Tarea:

Resuelve las siguientes ecuaciones y comprueben que las soluciones sean correctas:

a) 3(x-1) = 9

b) 2(3x+2) = 40

c) 4(3+2x) = 36

d) m-(7+m) = 3m+(m-3)

e) 2b+3(3b+1) = 25

f) 3 + 2(2x - 3) = 17

g) 3c - (4+2c) = 0

h) x-4(5-x) = 0

- Solución:

✤ Primera ecuación:

Resolvemos:

3 . (x - 1) = 9

3x - 3 = 9

3x = 9 + 3

3x = 12

x = 12 : 3

x = 4

Comprobamos:

3 . (x - 1) = 9

3 . (4 - 1) = 9

3 . 3 = 9

9 = 9

✤ Segunda ecuación:

Resolvemos:

2 . (3x + 2) = 40

6x + 4 = 40

6x = 40 - 4

6x = 36

x = 36 : 6

x = 6

Comprobamos:

2 . (3x + 2) = 40

2 . (3 . 6 + 2) = 40

2 . (18 + 2) = 40

2 . 20 = 40

40 = 40

✤ Tercera ecuación:

Resolvemos:

4 . (3 + 2x) = 36

12 + 8x = 36

8x = 36 - 12

8x = 24

x = 24 : 8

x = 3

Comprobamos:

4 . (3 + 2x) = 36

4 . (3 + 2 . 3) = 36

4 . (3 + 6) = 36

4 . 9 = 36

36 = 36

✤ Cuarta ecuación:

Resolvemos:

m - ( 7 + m) = 3m + (m - 3)

m - 7 - m = 3m + m - 3

0m - 7 = 4m - 3

-7 + 3 = 4m - 0m

-4 = 4m

-4 : 4 = m

-1 = m

Comprobamos:

m - ( 7 + m) = 3m + (m - 3)

-1 - (7 + -1) = 3 . -1 + (-1 - 3)

-1 - (7 - 1) = 3 . -1 + (-4)

-1 - 6 = -3 + (-4)

-7 = -3 - 4

-7 = -7

✤ Quinta ecuación:

Resolvemos:

2b + 3 . (3b + 1) = 25

2b + 9b + 3 = 25

11b + 3 = 25

11b = 25 - 3

11b = 22

b = 22 : 11

b = 2

Comprobamos:

2b + 3 . (3b + 1) = 25

2 . 2 + 3 . (3 . 2 + 1) = 25

2 . 2 + 3 . (6 + 1) = 25

2 . 2 + 3 . 7 = 25

4 + 21 = 25

25 = 25

✤ Sexta ecuación:

Resolvemos:

3 + 2 . (2x - 3) = 17

3 + 4x - 6 = 17

3 + 4x = 17 + 6

3 + 4x = 23

4x = 23 - 3

4x = 20

x = 20 : 4

x = 5

Comprobamos:

3 + 2 . ( 2x - 3) = 17

3 + 2 . ( 2 . 5 - 3) = 17

3 + 2 . (10 - 3) = 17

3 + 2 . 7 = 17

3 + 14 = 17

17 = 17

✤ Séptima ecuación:

Resolvemos:

3c - (4 + 2c) = 0

3c - 4 - 2c = 0

1c - 4 = 0

1c = 0 + 4

1c = 4

c = 4

Comprobamos:

3c - (4 + 2c) = 0

3 . 4 - (4 + 2 . 4) = 0

3 . 4 - (4 + 8) = 0

3 . 4 - 12 = 0

12 - 12 = 0

0 = 0

✤ Octava ecuación:

Resolvemos:

x - 4 . (5 - x) = 0

x - 20 + 4x = 0

5x - 20 = 0

5x = 0 + 20

5x = 20

x = 20 : 5

x = 4

Comprobamos:

x - 4 . (5 - x ) = 0

4 - 4 . (5 - 4) = 0

4 - 4 . 1 = 0

4 - 4 = 0

0 = 0