Question

Solve the inequality. (Enter your answer using interval notation.) 0 < |x − 8| < 1/2

Answer 1

To solve the inequality |x - 8| < 1/2, break it down into two separate inequalities: x - 8 < 1/2 and -(x - 8) < 1/2. Solve each inequality separately and combine the solutions to get the interval notation for the solution.

Step-by-step explanation:

To solve the inequality |x - 8| < 1/2, we can break it down into two separate inequalities:

1. x - 8 < 1/2
2. -(x - 8) < 1/2

Solving the first inequality, we add 8 to both sides and get x < 8.5.

Solving the second inequality, we distribute the negative sign and get -x + 8 < 1/2. Then we subtract 8 from both sides and get -x < -7.5. Multiplying both sides by -1, we have x > 7.5.

Combining the two solutions, we have 7.5 < x < 8.5. This is the interval notation for the solution to the inequality.