Question

solve the following inequality. write the solution set using interval notation.
-x > -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. use integers or fractions for any numbers in the expression.)
b. the solution set is ∅.

Explanation:

Step1: Multiply both sides by -1

When multiplying an inequality by a negative number, reverse the inequality sign:
$$(-1) \times (-x) < (-1) \times (-8)$$

Step2: Simplify both sides

Calculate the products to isolate $x$:
$$x < 8$$

Step3: Write in interval notation

All real numbers less than 8 correspond to the interval from negative infinity to 8, not including 8.
$$(-\infty, 8)$$

Answer:

A. The solution set is $(-\infty, 8)$