Question

Resuelve las siguientes ecuaciones de primer grado con una incógnita y valor absoluto
a.|5-2x|=14
b.|3x+7|=5x+13

Answer 1

Respuesta:

A) | 5-2x | = 14

5-2x = - 14 ó 5-2x = 14

5-2x-5 = -14-5 ó 5-2x-5 = 14-5

-2x = -19. ó. -2x = 9

-(-2x) = -(-19) ô -2x/-1 = 9/-1

2x = 19 ó 2x = -9

2x/2 = 19/2 ó 2x/2 = -9/2

X1 = 19/2 ó X2 = -9/2

B) | 3x+7 | = 5x+13

3x+7 = -(5x+13) ó 3x+7 = 5x+13

3x+7 = -5x-13 ó 3x+7 = 5x+13.

3x+7-3x = -5x-13-3x ó 3x+7-3x = 5x+13-3x

7 = -8x-13 ó 7 = 2x+13

7+13 = -8x-13+13 ó 7-2x = 2x-13+2x

20 = -8x ó 7-2x = -13

-8x = 20 ó -2x+7 = -13

-8x/-1 = 20/-1 ó -2x+7+13 = -13+13

8x = -20 ó -2x+20 = 0

8x/4 = -20/4 ó -2x/2+20/2 =0

2x = -5 ó -x+10 = 0

2x/2 = -5/2 ó -x = -10

2x/2 = -5/2 ó -(-x) = -(-10)

X1 = -5/2 ó X2 = 10

Explicación paso a paso: