Solve  2|7 – x| < 2 for x.

Sure, let's solve the inequality step by step.

1. We start with the given inequality: 2|7 – x| < 2

2. Divide both sides by 2 to isolate the absolute value: |7 – x| < 1

3. Now, we can split this into two separate inequalities. The absolute value of a number being less than 1 means the number is between -1 and 1. So, we have -1 < 7 - x < 1

4. We can solve these two inequalities separately:

   For -1 < 7 - x, subtract 7 from both sides to get -8 < -x, then multiply by -1 to get x < 8 (remember to flip the inequality when multiplying by a negative number)

   For 7 - x < 1, subtract 7 from both sides to get -x < -6, then multiply by -1 to get x > 6

5. So, the solution to the inequality 2|7 – x| < 2 is 6 < x < 8. This means x is greater than 6 and less than 8.