Question

4/3 z-2/5=7/5 z-1/10 cual es el valor de Z
nota: el signo / representa una fraccion

Answer 1

Respuesta:

Answer: z = (-9)/2

Explicación paso a paso:

Solve for z:

(4 z)/3 - 2/5 = (7 z)/5 - 1/10

Put each term in (4 z)/3 - 2/5 over the common denominator 15: (4 z)/3 - 2/5 = (20 z)/15 - 6/15:

((20 z)/15 - 6/15) = (7 z)/5 - 1/10

(20 z)/15 - 6/15 = (20 z - 6)/15:

((20 z - 6)/15) = (7 z)/5 - 1/10

Put each term in (7 z)/5 - 1/10 over the common denominator 10: (7 z)/5 - 1/10 = (14 z)/10 - 1/10:

(20 z - 6)/15 = ((14 z)/10 - 1/10)

(14 z)/10 - 1/10 = (14 z - 1)/10:

(20 z - 6)/15 = (1/10 (14 z - 1))

Multiply both sides by 30:

(30 (20 z - 6))/15 = (30 (14 z - 1))/10

30/15 = (15×2)/15 = 2:

2 (20 z - 6) = (30 (14 z - 1))/10

30/10 = (10×3)/10 = 3:

2 (20 z - 6) = 3 (14 z - 1)

Expand out terms of the left hand side:

(40 z - 12) = 3 (14 z - 1)

Expand out terms of the right hand side:

40 z - 12 = (42 z - 3)

Subtract 42 z from both sides:

(40 z - 42 z) - 12 = (42 z - 42 z) - 3

40 z - 42 z = -2 z:

-2 z - 12 = (42 z - 42 z) - 3

42 z - 42 z = 0:

-2 z - 12 = -3

Add 12 to both sides:

(12 - 12) - 2 z = 12 - 3

12 - 12 = 0:

-2 z = 12 - 3

12 - 3 = 9:

-2 z = 9

Divide both sides of -2 z = 9 by -2:

(-2 z)/(-2) = 9/(-2)

(-2)/(-2) = 1:

z = 9/(-2)

Multiply numerator and denominator of 9/(-2) by -1: