Answer
The equation we found was $\frac{3}{4}x - 3 = \frac{1}{2}x$.
$$x = 12$$
Work Step by Step
Let us translate this statement into an algebraic equation we can solve.
"$3$ is subtracted from three-fourths of a number" means:
$$\frac{3}{4}x - 3$$
The result of this expression is equal to "one-half of the number" means:
$$ = \frac{1}{2}x$$
We already have both sides of the equation, so let us put them together:
$$\frac{3}{4}x - 3 = \frac{1}{2}x$$
Now, we can solve for $x$ to find that unknown number:
Add $3$ to both sides of the equation to get the constant on one side of the equation first:
$$\frac{3}{4}x = \frac{1}{2}x + 3$$
Now, subtract $\frac{1}{2}x$ to isolate variables to the other side of the equation:
$$\frac{3}{4}x - \frac{1}{2}x = 3$$
To subtract fractions, we need to find the lowest common denominator of the two fractions. In this case, the lowest common denominator is $4$, so we multiply the terms on both sides of the equation by $4$ to get rid of the fractions:
$$4(\frac{3}{4}x) - 4(\frac{1}{2}x) = 4(3)$$
Divide out common factors to get rid of the fractions:
$$3x - 2x = 4(3)$$
Multiply on the right-hand side to simplify:
$$3x - 2x = 12$$
Subtract to solve for $x$:
$$x = 12$$