Question

Resolva a equação x-2/3x+2x-1/2=5x+2/6

Answer 1

Resposta:

x = -5/16

x = -0.3125

Explicação passo-a-passo:

Solve for x:

2 x + x - (2 x)/3 - 1/2 = 5 x + 2/6

The gcd of 2 and 6 is 2, so 2/6 = (2×1)/(2×3) = 2/2×1/3 = 1/3:

2 x + x - (2 x)/3 - 1/2 = 5 x + 1/3

Put each term in 2 x + x - (2 x)/3 - 1/2 over the common denominator 6: 2 x + x - (2 x)/3 - 1/2 = (12 x)/6 + (6 x)/6 - (4 x)/6 - 3/6:

(12 x)/6 + (6 x)/6 - (4 x)/6 - 3/6 = 5 x + 1/3

(12 x)/6 + (6 x)/6 - (4 x)/6 - 3/6 = (12 x + 6 x - 4 x - 3)/6:

(12 x + 6 x - 4 x - 3)/6 = 5 x + 1/3

6 x - 4 x + 12 x = 14 x:

(14 x - 3)/6 = 5 x + 1/3

Put each term in 5 x + 1/3 over the common denominator 3: 5 x + 1/3 = (15 x)/3 + 1/3:

(14 x - 3)/6 = (15 x)/3 + 1/3

(15 x)/3 + 1/3 = (15 x + 1)/3:

(14 x - 3)/6 = (15 x + 1)/3

Multiply both sides by 6:

(6 (14 x - 3))/6 = (6 (15 x + 1))/3

(6 (14 x - 3))/6 = 6/6×(14 x - 3) = 14 x - 3:

14 x - 3 = (6 (15 x + 1))/3

6/3 = (3×2)/3 = 2:

14 x - 3 = 2 (15 x + 1)

Expand out terms of the right hand side:

14 x - 3 = 30 x + 2

Subtract 30 x from both sides:

(14 x - 30 x) - 3 = (30 x - 30 x) + 2

14 x - 30 x = -16 x:

-16 x - 3 = (30 x - 30 x) + 2

30 x - 30 x = 0:

-16 x - 3 = 2

Add 3 to both sides:

(3 - 3) - 16 x = 3 + 2

3 - 3 = 0:

-16 x = 2 + 3

2 + 3 = 5:

-16 x = 5

Divide both sides of -16 x = 5 by -16:

(-16 x)/(-16) = 5/(-16)

(-16)/(-16) = 1:

x = 5/(-16)

Multiply numerator and denominator of 5/(-16) by -1:

Answer: |

| x = (-5)/16