Question

Simplify the expression

(3/4x -1/2) - (1/4x- 3/2)

Answer 1

MULTIPLY OUT the minus sign.
and you get: 3/4x - 1/2 - 1/4x + 3/2

then do simple addition/subtraction and you get:
2/4x + 2/2
then simplify, and you get:
1/2x + 1

Answer 2

((3)/(4)*x-(1)/(2))-((1)/(4)*x-(3)/(2))

Multiply (3)/(4) by x to get (3x)/(4).
((3x)/(4)-(1)/(2))-((1)/(4)*x-(3)/(2))

Multiply (1)/(4) by x to get (x)/(4).
((3x)/(4)-(1)/(2))-((x)/(4)-(3)/(2))

Multiply -1 by each term inside the parentheses.
((3x)/(4)-(1)/(2))-(x)/(4)+(3)/(2)

Remove the parentheses around the expression (3x)/(4)-(1)/(2).
(3x)/(4)-(1)/(2)-(x)/(4)+(3)/(2)

Combine the numerators of all expressions that have common denominators.
(3x-x)/(4)-(1)/(2)+(3)/(2)

Combine all like terms in the numerator.
(2x)/(4)-(1)/(2)+(3)/(2)

Reduce the expression (2x)/(4) by removing a factor of 2 from the numerator and denominator.
(x)/(2)-(1)/(2)+(3)/(2)

Combine the numerators of all expressions that have common denominators.
(x-1)/(2)+(3)/(2)

Combine the numerators of all expressions that have common denominators.
((x-1)+3)/(2)

Combine all like terms in the numerator.
(x+2)/(2)

Answer 3

\[(\frac{3}{4} * x - \frac{1}{2}) - (\frac{1}{4} * x - \frac{3}{2}) = \frac{2}{4} * x + \frac{2}{2} = \frac{1}{2}*x + 1\]

Answer 4

\[= \frac{x}{2} + 1 = \frac{x+2}{2}\]