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
Step 1: Simplify the left side of the inequality. 3x - (1)/(4) ((1)/(2)) > (1)/(4) - x Multiply the fractions on the left side: 3x - (1)/(8) > (1)/(4) - x Step 2: Gather all terms containing x on one side and constant terms on the other side. Add x to both sides of the inequality: 3x + x - (1)/(8) > (1)/(4) 4x - (1)/(8) > (1)/(4) Add (1)/(8) to both sides of the inequality: 4x > (1)/(4) + (1)/(8) Step 3: Combine the constant terms on the right side. Find a common denominator for (1)/(4) and (1)/(8), which is 8. (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) Now add the fractions: 4x > (2)/(8) + (1)/(8) 4x > (3)/(8) Step 4: Solve for x. Divide both sides by 4: x > (3)/(8 × 4) x > (3)/(32) Step 5: Express the solution as an interval. The inequality x > (3)/(32) means that x can be any value strictly greater than (3)/(32). In interval notation, this is written as: ((3)/(32), )