Question

|4x - 11| > -1. Solve the following linear inequality.

Answer 1

To solve the inequality |4x - 11| > -1, consider two cases: when 4x - 11 is positive and when it is negative. Solve for x in each case and the resulting solutions will satisfy the inequality.

Step-by-step explanation:

To solve the inequality |4x - 11| > -1, we need to consider two cases:

1. When 4x - 11 is positive: In this case, the inequality becomes 4x - 11 > -1. Solve for x by adding 11 to both sides and then dividing by 4.
2. When 4x - 11 is negative: In this case, the inequality becomes -(4x - 11) > -1. Simplify by distributing the negative sign and then solve for x by adding 11 to both sides and dividing by -4.

For both cases, the resulting solutions will satisfy the given inequality.