Question

`\mathrm{8(4u-1)-12u=11(2u-6)}`

Answer 1

u = 29

Explanation:

Solve for u:

8 (4 u - 1) - 12 u = 11 (2 u - 6)

8 (4 u - 1) = 32 u - 8:

(32 u - 8) - 12 u = 11 (2 u - 6)

Grouping like terms, 32 u - 12 u - 8 = (32 u - 12 u) - 8:

((32 u - 12 u) - 8) = 11 (2 u - 6)

32 u - 12 u = 20 u:

20 u - 8 = 11 (2 u - 6)

Expand out terms of the right hand side:

20 u - 8 = (22 u - 66)

Subtract 22 u from both sides:

(20 u - 22 u) - 8 = (22 u - 22 u) - 66

20 u - 22 u = -2 u:

-2 u - 8 = (22 u - 22 u) - 66

22 u - 22 u = 0:

-2 u - 8 = -66

Add 8 to both sides:

(8 - 8) - 2 u = 8 - 66

8 - 8 = 0:

-2 u = 8 - 66

8 - 66 = -58:

-2 u = -58

Divide both sides of -2 u = -58 by -2:

(-2 u)/(-2) = (-58)/(-2)

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

u = (-58)/(-2)

The gcd of -58 and -2 is -2, so (-58)/(-2) = (-2×29)/(-2×1) = (-2)/(-2)×29 = 29:

Answer: u = 29

Answer 2

29

Explanation:

To solve the equation for u, we need to get all the terms with u on one side of the equation and all the other constants on the other side. We can start by distributing the constants on the left side of the equation:

8(4u - 1) - 12u = 11(2u - 6)

8(4u - 1) - 12u = 22u - 66

32u - 8 - 12u = 22u - 66

20u - 8 = 22u - 66

Then we can combine like terms:

20u = 22u - 58

2u = 58

u = 29

The solution for u is 29.