Question

graph the solution. choose the correct graph below.
-16 ≤ 3x - 1 ≤ 8
write the solution set using set - builder notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. {x | - 5 ≤ x ≤ 3}
b. (use one inequality to express your answer if possible. for answers with more than one inequality that cannot be expressed by a single inequality, separate the inequalities by a comma. do not include the word or in your answer.)
the solution set is all real numbers.
c. the solution set is the empty set.
write the solution set using interval notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is □. (type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is the empty set.

Explanation:

Step1: Solve the inequality

Solve \(-16\leq3x - 1\leq8\).
First, add \(1\) to all parts: \(-16 + 1\leq3x-1 + 1\leq8 + 1\), which simplifies to \(-15\leq3x\leq9\).
Then divide all parts by \(3\): \(\frac{-15}{3}\leq\frac{3x}{3}\leq\frac{9}{3}\), so \(-5\leq x\leq3\).

Step2: Analyze the graph

The graph of \(x\) such that \(-5\leq x\leq3\) has a closed - circle at \(x=-5\) (because the inequality includes equality for \(x = - 5\), i.e., \(-16=3\times(-5)-1=-15 - 1=-16\)) and a closed - circle at \(x = 3\) (because \(3\times3-1=9 - 1=8\)). The line segment connects these two points.

Answer:

A. \(\{x|-5\leq x\leq3\}\); the graph corresponding to \(-5\leq x\leq3\) (with closed - circles at \(-5\) and \(3\) and a line segment between them)