Question

solve the compound inequality.
5(x - 4) < 25 or x + 7 > 8
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(type your answer in interval notation. simplify your answer. use integers or fractions for any
b. the solution set is ∅.

Explanation:

Step1: Solve \(5(x - 4) < 25\)

Divide both sides by 5: \(x - 4 < \frac{25}{5}\)
Simplify: \(x - 4 < 5\)
Add 4 to both sides: \(x < 5 + 4\)
So, \(x < 9\)

Step2: Solve \(x + 7 > 8\)

Subtract 7 from both sides: \(x > 8 - 7\)
So, \(x > 1\)

Step3: Combine the solutions (since it's "or")

The solution to \(5(x - 4) < 25\) or \(x + 7 > 8\) is all real numbers because the union of \(x < 9\) and \(x > 1\) covers all real numbers. In interval notation, this is \((-\infty, \infty)\)

Answer:

The solution set is \((-\infty, \infty)\)