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Problemario 3.1. Ecuaciones Lineales

1) Ecuaciones lineales con una incógnita:

a) 2x + 1 = 7

2x = 7 – 1

2x = 6

x = 3

Comprobamos: sustituimos el valor hallado de x enla ecuación original: 2(3) + 1 = 7

6 + 1 = 7

→ 7 = 7 identidad.

b) 6 ( x – ½ ) = 2x – 1

6x – 6(1/2) = 2x – 1

6x – 3 = 2x – 1

6x – 2x = -1 + 3

4x = 2

x = ½Comprobamos: sustituimos el valor hallado de x en la ecuación original: 6(1/2 – ½) = 2(1/2) – 1

(6/2 – 6/2) = 2/2 – 1

→ 0 = 0 identidad.

c) 5 ( x + 1 ) - x = 4x + 15

5 ( x + 1 ) - x = 4x + 155x + 5 – x = 4x + 15

( 5 – 1 ) x +5 = 4x + 15

4x + 5 = 4x + 15

0 x = 10

x = 10 / 0 La ecuación no tiene solución.

En las ecuaciones dadas compruebe el resultado:

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