\( \mid \& \quad \) Solve and check the linear equation. \[ 4 x+7=31 \] 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 \( \} \). The solution set is \( \varnothing \).

To solve the equation \( 4x + 7 = 31 \), we start by isolating \( x \). First, subtract 7 from both sides: \[ 4x = 31 - 7 \] This simplifies to: \[ 4x = 24 \] Now, divide both sides by 4: \[ x = \frac{24}{4} \] Hence, \( x = 6 \). Now, to check our solution, we substitute \( x = 6 \) back into the original equation: \[ 4(6) + 7 = 31 \] This simplifies to: \[ 24 + 7 = 31 \] Since \( 31 = 31 \) is true, our solution is verified! Thus, the correct choice is A. The solution set is \( \{6\} \). In ancient times, mathematicians often used methods similar to today’s algebra to solve problems. For instance, the Egyptians employed a system of hieroglyphs to express and manipulate equations akin to linear equations, showcasing the historical roots of our mathematical practices. Mathematics is not just an abstract concept; it has real-world applications! Linear equations, like the one we solved, can represent countless scenarios, from budgeting for your next shopping spree to determining the trajectory of a rocket. Understanding how to solve them empowers you in countless aspects of everyday life!