Question

4/3 (x+1)+1/8 (3x-1)=3/2 (2x-7)+5,5

Answer 1

4/3 (x+1)+1/8
32+3(x+1)/24(x+1)
32+3x+3/24x+24
35+3x/24x+24

(3x-1)=3/2
3x=3/2+1
3x=5/6
x=5/6 


(2x-7)+5,5 = 2x-7+5.5 = 2х-1.5

Answer 2

To solve the equation:

4/3(x + 1) + 1/8(3x - 1) = 3/2(2x - 7) + 5.5

Let's simplify and solve step by step:

Step 1: Distribute the fractions on both sides of the equation.

(4/3)(x + 1) + (1/8)(3x - 1) = (3/2)(2x - 7) + 5.5

(4/3)x + 4/3 + (1/8)(3x) - 1/8 = (3/2)(2x) - (3/2)(7) + 5.5

(4/3)x + 4/3 + (3/8)x - 1/8 = (3/2)(2x) - (21/2) + 5.5

Step 2: Combine like terms.

(4/3)x + (3/8)x + 4/3 - 1/8 = (3/2)(2x) - (21/2) + 5.5

[(32/24)x + (9/24)x] + (32/24) - (3/24) = (3/2)(2x) - (21/2) + 5.5

(41/24)x + (29/24) = (3/2)(2x) - (21/2) + 5.5

Step 3: Convert the mixed numbers to improper fractions.

(41/24)x + (29/24) = (3/2)(2x) - (21/2) + (55/10)

Step 4: Simplify the fractions.

(41/24)x + (29/24) = (3/2)(2x) - (21/2) + (55/10)

(41/24)x + (29/24) = (3/1)x - (21/2) + (55/10)

(41/24)x + (29/24) = (3/1)x - (21/1) + (55/10)

Step 5: Get rid of the fractions by multiplying through by the common denominator, which is 24 in this case.

24 * [(41/24)x + (29/24)] = 24 * [(3/1)x - (21/1) + (55/10)]

41x + 29 = 72x - 504 + 132

Step 6: Combine like terms.

41x + 29 = 72x - 372

Step 7: Move all the terms involving 'x' to one side of the equation.

41x - 72x = -372 - 29

-31x = -401

Step 8: Solve for 'x' by dividing both sides by -31.

x = (-401)/(-31)

x ≈ 12.935

Therefore, the solution to the equation is x ≈ 12.935.