Question

solve and graph. |x - 1| < 15. write the solution using set - builder notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice. {x| (simplify your answer. use integers or fractions for any numbers in the expression. 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.) a. the solution set is all real numbers. b. the solution set is the empty set. c. the solution set is

Explanation:

Step1: Recall absolute - value inequality rule

For \(|u|\lt a\) (\(a>0\)), the equivalent compound - inequality is \(-a\lt u\lt a\). Here \(u = x - 1\) and \(a = 15\), so we have \(-15\lt x - 1\lt15\).

Step2: Solve the compound - inequality

Add 1 to all parts of the inequality: \(-15+1\lt x-1 + 1\lt15 + 1\), which simplifies to \(-14\lt x\lt16\).

Step3: Write in set - builder notation

The solution in set - builder notation is \(\{x|-14\lt x\lt16\}\).

Answer:

The solution in set - builder notation is \(\{x|-14\lt x\lt16\}\). The graph would be a number line with an open circle at \(x=-14\) and an open circle at \(x = 16\), and the line segment between them shaded.