Question

Solve for x X - 1/2 (8 - x) = x + 3(4 - x) - x A) -32/9 B) -9/32 C) 32/9 D) 9/32

Answer 1

Option C

$x = \frac{32}{9}$

Solution:

$x - \frac{1}{2} \times (8 - x) = x + 3(4 - x) - x$

We have to solve for "x"

From given,

$x - \frac{1}{2} \times (8 - x) = x + 3(4 - x) - x$

Solve for brackets

Use distributive property

a(b + c) = ab + ac

Therefore,

$x - 4 + \frac{x}{2} = x + 12 - 3x - x$

Combine the constants

$x + \frac{x}{2} = x - x - 3x + 12 + 4\\\\x + \frac{x}{2} = -3x + 16$

Move the variables to left side of equation

$x + \frac{x}{2} + 3x = 16$

Combine the like terms

$2x + x + 6x = 32\\\\9x = 32\\\\x = \frac{32}{9}$

Thus option C is correct