Problem 90 - College Algebra Essentials

Question

Solve each absolute value inequality. $$4<|2-x|$$

Step-by-Step Solution

Answer

The solution to the inequality \(4<|2-x|\) is \( x < -2\) or \( x > 6\).

Step 1: Define the two inequalities

An absolute value inequality splits into two separate inequalities. In this case, the inequality \(4<|2-x|\) splits into \(2-x< -4\) and \(2-x > 4\).

Step 2: Solve the first inequality

Solving for \( x \) in the inequality \(2-x< -4\) gives \(x > 6\).

Step 3: Solve the second inequality

Solving for \( x \) in the inequality \(2-x > 4\) gives \(x < -2\).

Step 4: Write the final solution

For \(4<|2-x|\), \( x \) must be less than -2 or greater than 6.