Solve the linear equation. \[ 5 x+1=3 x+37 \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). B. The solution set is \( \{x \mid x \) is a real number \( \} \). c. The solution set is \( \varnothing \).

To solve the equation \( 5x + 1 = 3x + 37 \), first, we'll isolate \( x \). Start by subtracting \( 3x \) from both sides: \[ 5x - 3x + 1 = 37 \] This simplifies to: \[ 2x + 1 = 37 \] Next, subtract 1 from both sides: \[ 2x = 36 \] Now, divide both sides by 2: \[ x = 18 \] Thus, the solution is \( \{18\} \). So the correct choice is not listed, but if we were to restructure it, it would be a specific element rather than one of the given options. Now for the additional info: The idea of balancing equations is a classic skill that dates back to ancient civilizations, notably in Egypt and Babylon, where mathematicians solved problems involving equalities. This was the beginning of algebra as we know it today! In real life, solving linear equations is useful for budgeting, construction, and even cooking! Balancing costs in a shopping list or adjusting recipes can easily be done through these equations. Just think: if a recipe calls for 5x eggs and you want to double it, you simply set up a new equation to find your new quantity!