Solve for \( r:-12 b=10 r \)

To solve for \( r \), start by isolating \( r \) in the equation \( -12 b = 10 r \). You can do this by dividing both sides of the equation by 10: \[ r = \frac{-12 b}{10} \] Now, simplify the fraction: \[ r = -\frac{12}{10} b = -\frac{6}{5} b \] So, \( r = -\frac{6}{5} b \). If you find yourself facing similar problems, remember that isolating the variable can often involve basic algebraic operations like addition, subtraction, multiplication, or division. Just keep an eye on maintaining equality throughout the process! Common mistakes include forgetting to reverse the sign when you divide both sides by a negative number or mismanaging your fractions. Always double-check your signs and simplify when possible to avoid confusion!