Question

quiz: practice for exam 4
1 of 22
this quiz: 22 point(s) possible
this question: 1 point(s) possible
solve the inequality -4x - 21 < 11.

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 is the empty set.

Explanation:

Step1: Add 21 to both sides

To isolate the term with \( x \), we add 21 to both sides of the inequality \( -4x - 21 < 11 \). This gives us \( -4x - 21 + 21 < 11 + 21 \), which simplifies to \( -4x < 32 \).

Step2: Divide by -4 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. Dividing both sides of \( -4x < 32 \) by -4, we get \( x > \frac{32}{-4} \), which simplifies to \( x > -8 \).

Step3: Write in interval notation

The solution \( x > -8 \) in interval notation is \( (-8, \infty) \).

Answer:

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