Question

4x−3/2 − 5−2x/3 − 3x−4/3 =5

Answer 1

Answer:

x = 77/2

Step-by-step explanation:

Solve for x:

4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 = 5

Put each term in 4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 over the common denominator 6: 4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 = (24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6:

(24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6 = 5

(24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6 = (24 x - 4 x - 18 x - 30 - 9 - 8)/6:

(24 x - 4 x - 18 x - 30 - 9 - 8)/6 = 5

Grouping like terms, 24 x - 4 x - 18 x - 30 - 9 - 8 = (24 x - 4 x - 18 x) + (-9 - 30 - 8):

((24 x - 4 x - 18 x) + (-9 - 30 - 8))/6 = 5

24 x - 4 x - 18 x = 2 x:

(2 x + (-9 - 30 - 8))/6 = 5

-9 - 30 - 8 = -47:

(2 x + -47)/6 = 5

Multiply both sides of (2 x - 47)/6 = 5 by 6:

(6 (2 x - 47))/6 = 6×5

(6 (2 x - 47))/6 = 6/6×(2 x - 47) = 2 x - 47:

2 x - 47 = 6×5

6×5 = 30:

2 x - 47 = 30

Add 47 to both sides:

2 x + (47 - 47) = 47 + 30

47 - 47 = 0:

2 x = 30 + 47

30 + 47 = 77:

2 x = 77

Divide both sides of 2 x = 77 by 2:

(2 x)/2 = 77/2

2/2 = 1:

Answer:  x = 77/2