(J) \( 22=\frac{2 t}{t+8}, t \neq-8 \) (iPorque')

To solve the equation \( 22=\frac{2 t}{t+8} \), start by cross-multiplying to eliminate the fraction: \( 22(t + 8) = 2t \). Expanding gives you \( 22t + 176 = 2t \). Now, rearrange the equation to gather all terms involving \( t \) on one side: \( 22t - 2t = -176 \), which simplifies to \( 20t = -176 \). Dividing both sides by 20 yields \( t = -\frac{176}{20} \), or simplifying further, \( t = -8.8 \). Just remember to check your solution by substituting it back into the original equation to ensure it satisfies \( t \neq -8 \)! Many concepts in algebra come to life through real-world scenarios. Take this example of solving for \( t \) in an equation related to rates, like calculating speed or even mixing solutions. Often, equations used in physics and engineering can be modeled similarly. Understanding how variables interact helps in making sense of complex systems, from figuring out your water bill to optimizing a recipe for the perfect cake! Enjoy relating math to everyday life!