This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — I apologize if my previous responses came across as too direct. I'm here to help you learn! Let's work through some examples to understand how to solve inequalities. Example 1: Basic Linear Inequality Solve for x: 2x - 5 < 11 Step 1: Add 5 to both sides of the inequality. This uses the Addition Property of inequalities. 2x - 5 + 5 < 11 + 5 2x < 16 Step 2: Divide both sides by 2. Since 2 is a positive number, the direction of the inequality remains the same. This uses the Multiplication/Division Property. (2x)/(2) < (16)/(2) x < 8 The solution is all real numbers less than 8. x < 8 Example 2: Inequality with Multiplication/Division by a Negative Number Solve for x: -3x + 7 19 Step 1: Subtract 7 from both sides of the inequality. -3x + 7 - 7 19 - 7 -3x 12 Step 2: Divide both sides by -3. Since -3 is a negative number, we must reverse the direction of the inequality sign. (-3x)/(-3) (12)/(-3) x -4 The solution is all real numbers less than or equal to -4. x -4 Example 3: Inequality with Variables on Both Sides Solve for x: 4x + 3 2x - 9 Step 1: Subtract 2x from both sides to gather the x terms on one side. 4x + 3 - 2x 2x - 9 - 2x 2x + 3 -9 Step 2: Subtract 3 from both sides to isolate the x term. 2x + 3 - 3 -9 - 3 2x -12 Step 3: Divide both sides by 2. Since 2 is a positive number, the inequality direction remains the same. (2x)/(2) (-12)/(2) x -6 The solution is all real numbers less than or equal to -6. x -6 I hope these examples help clarify the concepts and rules! Send me the next one 📸