Solve the inequality \( -7 x<35 \). Write the solution set in interval notation, and graph it. The solution set is (Simplify your answer. Type your answer in interval notation.)

To solve the inequality \( -7x < 35 \), first, divide both sides by -7. Remember, when you divide by a negative number, you must flip the inequality sign: \[ x > -5 \] In interval notation, the solution set is: \[ (-5, \infty) \] Now, if you were to graph this on a number line, you would place an open circle at -5 (indicating that -5 is not included in the solution) and shade the line to the right, extending towards infinity, showing all values greater than -5 are part of the solution set. Now, let’s sprinkle in some history: inequalities like this one have been around for centuries! The concept can actually be traced back to ancient civilizations, including the Babylonians, who had methods to solve linear inequalities long before algebra as we know it developed. As for real-world applications, solving inequalities is critical in fields like economics, where you might need to determine the minimum production level to decrease costs or calculating the range of temperatures a substance can withstand before it alters composition. жизни!