Answer
The equation we came up with is:
$$\frac{7}{8}x - 30 = \frac{1}{2}x$$
Solving for $x$, we get:
$$x = 80$$
Work Step by Step
Let us translate this statement into an algebraic equation we can solve.
"$30$ is subtracted from seven-eighths of a number" means:
$$\frac{7}{8}x - 30$$
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:
$$\frac{7}{8}x - 30 = \frac{1}{2}x$$
Now, we can solve for $x$ to find that unknown number:
Add $30$ to both sides of the equation to get the constant on one side of the equation first:
$$\frac{7}{8}x = \frac{1}{2}x + 30$$
Now, subtract $\frac{1}{2}x$ to isolate variables to the other side of the equation:
$$\frac{7}{8}x - \frac{1}{2}x = 3$$
To subtract fractions, we need to find the lowest common denominator of the two fractions. In this case, the lowest common denominator is $8$, so we multiply the terms on both sides of the equation by $8$ to get rid of the fractions:
$$8(\frac{7}{8}x) - 8(\frac{1}{2}x) = 8(30)$$
Divide out common factors to get rid of the fractions:
$$7x - 4x = 8(30)$$
Multiply on the right-hand side to simplify:
$$7x - 4x = 240$$
Combine like terms on the left-hand side of the equation:
$$3x = 240$$
Divide both sides of the equation by $3$ to solve for $x$:
$$x = 80$$
