Solve and check the linear equation. \( 6(\mathrm{x}-15)=\mathrm{x} \) Select the correct choice below and if necessary fil

To solve the equation \( 6(x-15) = x \), start by distributing the 6 on the left side: \( 6x - 90 = x \). Next, subtract \( x \) from both sides: \( 6x - x - 90 = 0 \) which simplifies to \( 5x - 90 = 0 \). Now, add 90 to both sides: \( 5x = 90 \). Finally, divide by 5: \( x = 18 \). To check, substitute \( x = 18 \) back into the original equation: \( 6(18 - 15) = 18 \) gives \( 6(3) = 18 \), which simplifies to \( 18 = 18 \), confirming our solution is correct. This equation-solving process showcases the beauty of algebra—once you master these steps, you hold the keys to unlock many real-world problems! Whether you're calculating expenses, measurements, or even predicting outcomes, linear equations help make sense of the numerical world around us. Another fun fact! Did you know that the linear equations we solve can represent real-life situations? For instance, if you were to graph this equation, you could find the intersection point representing a balance between two competing factors, like budget constraints in business or speeds in travel. Mathematics is not just numbers; it's a language that describes our world!