SOLVE 4-4x=9-12r
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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To solve the equation $4 - 4x = 9 - 12r$, we can express one variable in terms of the other.
Step 1: Solve for $x$ in terms of $r$.
$$4 - 4x = 9 - 12r$$
Subtract 4 from both sides:
$$-4x = 9 - 12r - 4$$
$$-4x = 5 - 12r$$
Divide both sides by -4:
$$x = \frac{5 - 12r}{-4}$$
$$x = -\frac{5}{4} + \frac{12r}{4}$$
$$x = -\frac{5}{4} + 3r$$
Step 2: Solve for $r$ in terms of $x$.
$$4 - 4x = 9 - 12r$$
Subtract 9 from both sides:
$$4 - 4x - 9 = -12r$$
$$-5 - 4x = -12r$$
Divide both sides by -12:
$$\frac{-5 - 4x}{-12} = r$$
$$r = \frac{-5}{-12} + \frac{-4x}{-12}$$
$$r = \frac{5}{12} + \frac{4x}{12}$$
$$r = \frac{5}{12} + \frac{x}{3}$$
The solutions are:
$$ \boxed{x = 3r - \frac{5}{4}} \quad \text{or} \quad \boxed{r = \frac{x}{3} + \frac{5}{12}} $$
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