Question

solve the inequality algebraically. express your answer using set notation or interval notation. graph the solution set. verify your results using a graphing utility
|7x| < 42

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.

graph the solution set. choose the correct graph below

a. number line with open circle at -6 and 6, line between them

b. number line with closed brackets at -6 and 6, lines outside

c. number line with open circles at -6 and 6, lines outside

d. number line with closed brackets at -6 and 6, line between them

e. number line with line covering all

f. number line with no line

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|7x| < 42\), we apply this rule.

Step2: Solve the compound inequality

Divide all parts of \(-42 < 7x < 42\) by 7.
\(\frac{-42}{7}<\frac{7x}{7}<\frac{42}{7}\) simplifies to \(-6 < x < 6\).

Step3: Express in interval notation

The solution in interval notation is \((-6, 6)\).

Step4: Identify the correct graph

The graph should have open circles at -6 and 6 (since the inequality is strict, \(<\) not \(\leq\)) and a line connecting them. Looking at the options, option A has open circles at -6 and 6 with the line in between.

Answer:

The solution set in interval notation is \((-6, 6)\), so the correct choice for the solution set is A. The solution set is \(\boxed{(-6, 6)}\) and the correct graph is A.