Solve |1 - 4x| > 7

Sure, let's solve the inequality |1 - 4x| > 7 step by step.

Step 1: Split the inequality into two separate inequalities: 1 - 4x > 7 and 1 - 4x < -7

Step 2: Solve the first inequality: 1 - 4x > 7 Subtract 1 from both sides: -4x > 6 Divide both sides by -4 (remember to reverse the inequality when dividing by a negative number): x < -6/4 Simplify: x < -3/2

Step 3: Solve the second inequality: 1 - 4x < -7 Subtract 1 from both sides: -4x < -8 Divide both sides by -4 (remember to reverse the inequality when dividing by a negative number): x > 2

Step 4: Combine the solutions: The solution to the inequality |1 - 4x| > 7 is x < -3/2 or x > 2.