14) -4(16 + 8x) + 12(7 - 3x) = 50(x + 3) - (15 - x)

15) 96(x - 1) - (7x - 64) = 38(2 - x) + 3(17 + 2x) + 83

Let's solve the equations step-by-step.
Equation 1 :
− 4 ( 16 + 8 x ) + 12 ( 7 − 3 x ) = 50 ( x + 3 ) − ( 15 − x )

Distribute the terms:
− 4 × 16 = − 64
− 4 × 8 x = − 32 x
12 × 7 = 84
12 × − 3 x = − 36 x
50 × x = 50 x
50 × 3 = 150
− ( 15 − x ) = − 15 + x
Replace in the equation:
− 64 − 32 x + 84 − 36 x = 50 x + 150 − 15 + x

Combine like terms:
( − 64 + 84 ) + ( − 32 x − 36 x ) = ( 50 x + x ) + ( 150 − 15 )
20 − 68 x = 51 x + 135

Move all x terms to one side and constant terms to the other:
− 68 x − 51 x = 135 − 20

Simplify:
− 119 x = 115

Solve for x :
x = − 119 115 ​
x = − 119 115 ​


Equation 2 :
96 ( x − 1 ) − ( 7 x − 64 ) = 38 ( 2 − x ) + 3 ( 17 + 2 x ) + 83

Distribute the terms:
96 × x = 96 x
96 × − 1 = − 96
− ( 7 x − 64 ) = − 7 x + 64
38 × 2 = 76
38 × − x = − 38 x
3 × 17 = 51
3 × 2 x = 6 x
Replace in the equation:
96 x − 96 − 7 x + 64 = 76 − 38 x + 51 + 6 x + 83

Combine like terms:
( 96 x − 7 x ) + ( − 96 + 64 ) = ( 76 + 51 + 83 ) + ( − 38 x + 6 x )
89 x − 32 = 210 − 32 x

Move all x terms to one side and constant terms to the other:
89 x + 32 x = 210 + 32

Simplify:
121 x = 242

Solve for x :
x = 121 242 ​
x = 2


In summary, the solutions are:

For the first equation, x = − 119 115 ​ .

For the second equation, x = 2 .

Answered by RyanHarmon181 | 2025-07-06