Question

32
$x + 3 - x + 2 - x + 1 - (2 - x) - (x + 3) - x + 1$
is equivalent to
a $2x - 4$
b $2x + 4$
c $x - 4$
d none of these

Explanation:

Step1: Simplify innermost parentheses

$$x + 1 - (2 - x) - (x + 3) = x + 1 - 2 + x - x - 3$$
Combine like terms:
$$= (x + x - x) + (1 - 2 - 3) = x - 4$$

Step2: Substitute into middle brackets

$$x + 2 - (x - 4) - x + 1 = x + 2 - x + 4 - x + 1$$
Combine like terms:
$$= (x - x - x) + (2 + 4 + 1) = -x + 7$$

Step3: Substitute into outermost expression

$$x + 3 - (-x + 7)$$
Distribute the negative sign:
$$= x + 3 + x - 7$$
Combine like terms:
$$= (x + x) + (3 - 7) = 2x - 4$$

Answer:

A. $2x - 4$