Math Snap

STEP 1

1. The equation $5 - \frac{4}{x} = 7$ is a rational equation.
2. We will solve for $x$ by isolating the variable term.

STEP 2

1. Isolate the rational term $\frac{4}{x}$.
2. Solve for $x$.
3. Check for any restrictions on the solution.

STEP 3

First, subtract 5 from both sides of the equation to isolate the rational term:
$$5 - \frac{4}{x} = 7$$ $$-\frac{4}{x} = 7 - 5$$ $$-\frac{4}{x} = 2$$

STEP 4

Multiply both sides by $-1$ to make the fraction positive:
$$\frac{4}{x} = -2$$

STEP 5

To solve for $x$, multiply both sides by $x$ to eliminate the fraction:
$$4 = -2x$$

STEP 6

Now, divide both sides by $-2$ to solve for $x$:
$$x = \frac{4}{-2}$$ $$x = -2$$

Check for any restrictions. Since $x$ cannot be zero (as it would make the denominator zero), and $x = -2$ does not violate this restriction, it is a valid solution.
The solution set is:
$$\{-2\}$$